Finite Group Databasebeta

← C3×#17593 #10636200

Subgroups — C3×#17593 #10636200

Order 768.

1042 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3444C211yesmaximal, characteristic
2C3×#2920C211yesmaximal, characteristic, complemented
3C2×C3×#383C211yesmaximal, characteristic, complemented
4C3×#1521C214yesmaximal, complemented
5C3×#1515C212yesmaximal, complemented
6C3×#1514C212yesmaximal, complemented
7C3×#1504C214yesmaximal, complemented
8#17593C311yesmaximal, characteristic, direct product factor, Sylow
9C3×#533C411yescharacteristic, complemented
10C3×#533C411yescharacteristic, complemented
11C3×#533C2211yescharacteristic
12C3×#532C411yescharacteristic, complemented
13C3×#532C411yescharacteristic, complemented
14C3×#532C2211yescharacteristic
15C3×#529—21no—
16C3×#529—21no—
17C3×#529—21no—
18C3×#529—21no—
19C3×#529C412yescomplemented
20C3×#529C2212yes—
21C3×#525—21no—
22C3×#525—21no—
23C3×#525C2212yes—
24C3×C4×#41—21no—
25C3×C4×#41—21no—
26C3×C4×#41C412yescomplemented
27C22×C3×C42C2211yescharacteristic
28C3×#432—21no—
29C3×#432C2212yes—
30C3×#431—21no—
31C3×#431C2212yes—
32C3×#423—21no—
33C3×#407C2212yes—
34C3×C4×M16—21no—
35C3×#383—21no—
36C3×#383—21no—
37C3×#383C2212yes—
38C3×#383C2212yes—
39C2×C3×#95—21no—
40C2×C3×#95—21no—
41C2×C3×#95C2212yes—
42C3×#328C2218yes—
43C3×#327C2218yes—
44#3444C2×C311yescharacteristic
45#2920C2×C311yescharacteristic, complemented
46C2×#383C2×C311yescharacteristic, complemented
47#1521C2×C314yescomplemented
48#1515C2×C312yescomplemented
49#1514C2×C312yescomplemented
50#1504C2×C314yescomplemented
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41C2×C412yes—
54C23×C3×C4—22no—
55C23×C3×C4D411yescharacteristic
56C23×C3×C4D411yescharacteristic
57C23×C3×C4C2311yescharacteristic
58C2×C3×M16—22no—
59C3×C4⋊Q8C2×C411yescharacteristic, complemented
60C3×C4⋊Q8C2×C411yescharacteristic, complemented
61C3×C4⋊Q8C2×C411yescharacteristic, complemented
62C3×#127C2×C411yescharacteristic, complemented
63C3×#126—22no—
64C3×#126—22no—
65C3×#125—21no—
66C3×#125—21no—
67C3×#125C2×C412yescomplemented
68C3×#124—21no—
69C3×#124—21no—
70C3×#124C2×C412yescomplemented
71C3×#123—22no—
72C3×#123—22no—
73C3×#123—22no—
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8—21no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8C2×C412yes—
79C3×C22⋊Q8C2312yes—
80C3×#121—21no—
81C3×#121—21no—
82C3×#121—21no—
83C3×#121—21no—
84C3×#121C2×C412yes—
85C3×#121C2312yes—
86C3×#120—22no—
87C3×C4×Q8—21no—
88C3×C4×Q8—21no—
89C3×C4×Q8—21no—
90C3×C4×Q8—21no—
91C3×C4×Q8C2×C412yescomplemented
92C3×C4×Q8C2×C412yescomplemented
93C3×C4×D4—22no—
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4—21no—
100C3×C4×D4—21no—
101C3×C4×D4—21no—
102C3×C4×D4—21no—
103C3×C4×D4C2×C412yescomplemented
104C3×C4×D4C2×C412yescomplemented
105C3×#117—21no—
106C3×#117—21no—
107C3×#117—22no—
108C3×#117—22no—
109C3×#117—22no—
110C3×#117C2×C412yes—
111C2×C3×C42—22no—
112C2×C3×C42C2×C411yescharacteristic
113C2×C3×C42C2×C411yescharacteristic
114C2×C3×C42C2×C411yescharacteristic
115C2×C3×C42C2×C411yescharacteristic
116C2×C3×C42D411yescharacteristic
117C2×C3×C42D411yescharacteristic
118C2×C3×C42D411yescharacteristic
119C2×C3×C42D411yescharacteristic
120C2×C3×C42D411yescharacteristic
121C2×C3×C42D411yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C3×C4⋊C8—22no—
125C3×C4⋊C8—22no—
126C3×C22⋊C8—22no—
127C3×C22⋊C8C2314yes—
128C3×#97—22no—
129C3×C4×C8—22no—
130C3×#95—22no—
131C3×#95—22no—
132C3×#95—22no—
133C3×#95—22no—
134C3×#95—22no—
135C3×#95C2314yes—
136#533C3×C411yescharacteristic, complemented
137#533C3×C411yescharacteristic, complemented
138#533C22×C311yescharacteristic
139#532C3×C411yescharacteristic, complemented
140#532C3×C411yescharacteristic, complemented
141#532C22×C311yescharacteristic
142#529—21no—
143#529—21no—
144#529—21no—
145#529—21no—
146#529C3×C412yescomplemented
147#529C22×C312yes—
148#525—21no—
149#525—21no—
150#525C22×C312yes—
151C4×#41—21no—
152C4×#41—21no—
153C4×#41C3×C412yescomplemented
154C22×C42C22×C311yescharacteristic
155#432—21no—
156#432C22×C312yes—
157#431—21no—
158#431C22×C312yes—
159#423—21no—
160#407C22×C312yes—
161C4×M16—21no—
162#383—21no—
163#383—21no—
164#383C22×C312yes—
165#383C22×C312yes—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95C22×C312yes—
169#328C22×C318yes—
170#327C22×C318yes—
171C24×C3C2×D411yescharacteristic
172C3×#41—44no—
173C3×#41—44no—
174C3×#41—44no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8C22×C412yes—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4C22×C412yes—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—24no—
188C22×C3×C4—42no—
189C22×C3×C4—42no—
190C22×C3×C4—42no—
191C22×C3×C4—44no—
192C22×C3×C4—44no—
193C22×C3×C4—44no—
194C22×C3×C4C22⋊C411yescharacteristic
195C22×C3×C4C22⋊C411yescharacteristic
196C22×C3×C4C22⋊C411yescharacteristic
197C22×C3×C4C22⋊C411yescharacteristic
198C22×C3×C4C22⋊C411yescharacteristic
199C22×C3×C4C22⋊C411yescharacteristic
200C22×C3×C4C22⋊C411yescharacteristic
201C22×C3×C4C22⋊C411yescharacteristic
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C22×C411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2411yescharacteristic
212C3×M16—44no—
213C2×C3×C8—24no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4C22×C412yes—
225C3×C4⋊C4C22×C412yes—
226C3×C22⋊C4—22no—
227C3×C22⋊C4—22no—
228C3×C22⋊C4—22no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—22no—
231C3×C22⋊C4—22no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C42—22no—
236C3×C42—22no—
237C3×C42—22no—
238C3×C42C22⋊C411yescharacteristic
239C3×C42C22⋊C411yescharacteristic
240C3×C42C22⋊C411yescharacteristic
241C3×C42C22⋊C411yescharacteristic
242C3×C42C22⋊C411yescharacteristic
243C3×C42C22⋊C411yescharacteristic
244C3×C42C22⋊C411yescharacteristic
245C3×C42C22⋊C411yescharacteristic
246C3×C42C22×C411yescharacteristic
247C3×C42C22×C411yescharacteristic
248C3×C42C22×C411yescharacteristic
249C3×C42C22×C411yescharacteristic
250C3×C42C2×D411yescharacteristic
251C3×C42C2×D411yescharacteristic
252C3×C42C2×D411yescharacteristic
253C3×C42C2×D411yescharacteristic
254C2×#41—21no—
255C2×#41—21no—
256C2×#41C2×C3×C412yes—
257C23×C4—22no—
258C23×C4C3×D411yescharacteristic
259C23×C4C3×D411yescharacteristic
260C23×C4C23×C311yescharacteristic
261C2×M16—22no—
262C4⋊Q8C2×C3×C411yescharacteristic, complemented
263C4⋊Q8C2×C3×C411yescharacteristic, complemented
264C4⋊Q8C2×C3×C411yescharacteristic, complemented
265#127C2×C3×C411yescharacteristic, complemented
266#126—22no—
267#126—22no—
268#125—21no—
269#125—21no—
270#125C2×C3×C412yescomplemented
271#124—21no—
272#124—21no—
273#124C2×C3×C412yescomplemented
274#123—22no—
275#123—22no—
276#123—22no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8C2×C3×C412yes—
282C22⋊Q8C23×C312yes—
283#121—21no—
284#121—21no—
285#121—21no—
286#121—21no—
287#121C2×C3×C412yes—
288#121C23×C312yes—
289#120—22no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8C2×C3×C412yescomplemented
295C4×Q8C2×C3×C412yescomplemented
296C4×D4—22no—
297C4×D4—22no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C2×C3×C412yescomplemented
307C4×D4C2×C3×C412yescomplemented
308#117—21no—
309#117—21no—
310#117—22no—
311#117—22no—
312#117—22no—
313#117C2×C3×C412yes—
314C2×C42—22no—
315C2×C42C2×C3×C411yescharacteristic
316C2×C42C2×C3×C411yescharacteristic
317C2×C42C2×C3×C411yescharacteristic
318C2×C42C2×C3×C411yescharacteristic
319C2×C42C3×D411yescharacteristic
320C2×C42C3×D411yescharacteristic
321C2×C42C3×D411yescharacteristic
322C2×C42C3×D411yescharacteristic
323C2×C42C3×D411yescharacteristic
324C2×C42C3×D411yescharacteristic
325C2×C42C23×C311yescharacteristic
326C2×C42C23×C311yescharacteristic
327C4⋊C8—22no—
328C4⋊C8—22no—
329C22⋊C8—22no—
330C22⋊C8C23×C314yes—
331#97—22no—
332C4×C8—22no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95—22no—
338#95C23×C314yes—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3C2×C22⋊C411yescharacteristic
344C23×C3C2×C22⋊C411yescharacteristic
345C23×C3C22×D411yescharacteristic
346C3×Q8—42no—
347C3×Q8—42no—
348C3×Q8—42no—
349C3×D4—42no—
350C3×D4—42no—
351C3×D4—42no—
352C3×D4—44no—
353C3×D4—44no—
354C3×D4—44no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—44no—
377C2×C3×C4—44no—
378C2×C3×C4—44no—
379C2×C3×C4—44no—
380C2×C3×C4—44no—
381C2×C3×C4—44no—
382C2×C3×C4—88no—
383C2×C3×C4C2×C22⋊C411yescharacteristic
384C2×C3×C4C2×C22⋊C411yescharacteristic
385C2×C3×C4C2×C22⋊C411yescharacteristic
386C2×C3×C4C2×C22⋊C411yescharacteristic
387C2×C3×C4C2×C22⋊C411yescharacteristic
388C2×C3×C4C2×C22⋊C411yescharacteristic
389C2×C3×C4C2×C22⋊C411yescharacteristic
390C2×C3×C4C2×C22⋊C411yescharacteristic
391C2×C3×C4C2×C22⋊C411yescharacteristic
392C2×C3×C4C2×C22⋊C411yescharacteristic
393C2×C3×C4C23×C411yescharacteristic
394C2×C3×C4C22×D411yescharacteristic
395C3×C8—44no—
396C24C2×C3×D411yescharacteristic
397#41—44no—
398#41—44no—
399#41—44no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8C22×C3×C412yes—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4C22×C3×C412yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4C3×C22⋊C411yescharacteristic
420C22×C4C3×C22⋊C411yescharacteristic
421C22×C4C3×C22⋊C411yescharacteristic
422C22×C4C3×C22⋊C411yescharacteristic
423C22×C4C3×C22⋊C411yescharacteristic
424C22×C4C3×C22⋊C411yescharacteristic
425C22×C4C3×C22⋊C411yescharacteristic
426C22×C4C3×C22⋊C411yescharacteristic
427C22×C4C22×C3×C411yescharacteristic
428C22×C4C22×C3×C411yescharacteristic
429C22×C4C2×C3×D411yescharacteristic
430C22×C4C2×C3×D411yescharacteristic
431C22×C4C2×C3×D411yescharacteristic
432C22×C4C2×C3×D411yescharacteristic
433C22×C4C2×C3×D411yescharacteristic
434C22×C4C2×C3×D411yescharacteristic
435C22×C4C2×C3×D411yescharacteristic
436C22×C4C24×C311yescharacteristic
437M16—44no—
438C2×C8—24no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4C22×C3×C412yes—
450C4⋊C4C22×C3×C412yes—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C42—22no—
461C42—22no—
462C42—22no—
463C42C3×C22⋊C411yescharacteristic
464C42C3×C22⋊C411yescharacteristic
465C42C3×C22⋊C411yescharacteristic
466C42C3×C22⋊C411yescharacteristic
467C42C3×C22⋊C411yescharacteristic
468C42C3×C22⋊C411yescharacteristic
469C42C3×C22⋊C411yescharacteristic
470C42C3×C22⋊C411yescharacteristic
471C42C22×C3×C411yescharacteristic
472C42C22×C3×C411yescharacteristic
473C42C22×C3×C411yescharacteristic
474C42C22×C3×C411yescharacteristic
475C42C2×C3×D411yescharacteristic
476C42C2×C3×D411yescharacteristic
477C42C2×C3×D411yescharacteristic
478C42C2×C3×D411yescharacteristic
479C22×C3—28no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3#41012yes—
490C22×C3#42112yes—
491C22×C3C22×C22⋊C411yescharacteristic
492C22×C3#57512yes—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—42no—
506C3×C4—42no—
507C3×C4—42no—
508C3×C4—84no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23C2×C3×C22⋊C411yescharacteristic
514C23C2×C3×C22⋊C411yescharacteristic
515C23C22×C3×D411yescharacteristic
516Q8—42no—
517Q8—42no—
518Q8—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—44no—
523D4—44no—
524D4—44no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—88no—
553C2×C4C2×C3×C22⋊C411yescharacteristic
554C2×C4C2×C3×C22⋊C411yescharacteristic
555C2×C4C2×C3×C22⋊C411yescharacteristic
556C2×C4C2×C3×C22⋊C411yescharacteristic
557C2×C4C2×C3×C22⋊C411yescharacteristic
558C2×C4C2×C3×C22⋊C411yescharacteristic
559C2×C4C2×C3×C22⋊C411yescharacteristic
560C2×C4C2×C3×C22⋊C411yescharacteristic
561C2×C4C2×C3×C22⋊C411yescharacteristic
562C2×C4C2×C3×C22⋊C411yescharacteristic
563C2×C4C23×C3×C411yescharacteristic
564C2×C4C22×C3×D411yescharacteristic
565C8—44no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—22no—
569C2×C3—82no—
570C2×C3C2×#41011yescharacteristic
571C2×C3#289611yescharacteristic
572C2×C3C2×#42111yescharacteristic
573C22—28no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22C3×#41012yes—
584C22C3×#42112yes—
585C22C22×C3×C22⋊C411yescharacteristic
586C22C3×#57512yes—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—84no—
603C3#1759311yescharacteristic, direct product factor, Sylow
604C2—22no—
605C2—22no—
606C2—22no—
607C2—82no—
608C2C2×C3×#41011yescharacteristic
609C2C3×#289611yescharacteristic
610C2C2×C3×#42111yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3444C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C42 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#2920C2semidirect
3. C2×C3×#383C2semidirect
4. C3×#1521C2semidirect
5. C3×#1515C2semidirect
6. C3×#1514C2semidirect
7. C3×#1504C2semidirect
8. #17593C3direct (N × H)
9. C3×#533C4semidirect
10. C3×#533C4semidirect
12. C3×#532C4semidirect
13. C3×#532C4semidirect
19. C3×#529C4semidirect
26. C3×C4×#41C4semidirect
45. #2920C2×C3semidirect
46. C2×#383C2×C3semidirect
47. #1521C2×C3semidirect
48. #1515C2×C3semidirect
49. #1514C2×C3semidirect
50. #1504C2×C3semidirect
59. C3×C4⋊Q8C2×C4semidirect
60. C3×C4⋊Q8C2×C4semidirect
61. C3×C4⋊Q8C2×C4semidirect
62. C3×#127C2×C4semidirect
67. C3×#125C2×C4semidirect
70. C3×#124C2×C4semidirect
91. C3×C4×Q8C2×C4semidirect
92. C3×C4×Q8C2×C4semidirect
103. C3×C4×D4C2×C4semidirect
104. C3×C4×D4C2×C4semidirect
136. #533C3×C4semidirect
137. #533C3×C4semidirect
139. #532C3×C4semidirect
140. #532C3×C4semidirect
146. #529C3×C4semidirect
153. C4×#41C3×C4semidirect
262. C4⋊Q8C2×C3×C4semidirect
263. C4⋊Q8C2×C3×C4semidirect
264. C4⋊Q8C2×C3×C4semidirect
265. #127C2×C3×C4semidirect
270. #125C2×C3×C4semidirect
273. #124C2×C3×C4semidirect
294. C4×Q8C2×C3×C4semidirect
295. C4×Q8C2×C3×C4semidirect
306. C4×D4C2×C3×C4semidirect
307. C4×D4C2×C3×C4semidirect
603. C3#17593direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#34442
C3×#29202
C2×C3×#3832
C3×#15212
C3×#15152
C3×#15142
C3×#15042
#175933