Finite Group Databasebeta

← C2×D3×#4033 #14478854

Subgroups — C2×D3×#4033 #14478854

Order 1920.

3328 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic10C211yesmaximal, characteristic
2C2×#91776C211yesmaximal, characteristic, complemented
3C2×C5×D3×C4⋊C4C211yesmaximal, characteristic
4C2×C3×#4033C211yesmaximal, characteristic, complemented
5C2×D3×#683C212yesmaximal
6C2×C4×D3×Dic5C211yesmaximal, characteristic
7C2×C4×D3×Dic5C212yesmaximal
8C2×#91333C211yesmaximal, characteristic, complemented
9C2×#91331C211yesmaximal, characteristic, complemented
10C2×#91325C212yesmaximal, complemented
11C2×#91323C212yesmaximal, complemented
12D3×#4033C2116yesmaximal, direct product factor
13C22×#4033—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×C4×C5×D3C2211yescharacteristic
17C22×C3×Dic10C2211yescharacteristic
18C22×#1204C2212yes—
19C22×D3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2212yes—
21C22×D3×Dic5C2211yescharacteristic
22C2×D3×Dic10C4116yescomplemented
23C2×D3×Dic10C2218yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×#6712C2212yes—
26C2×C4×Dic15C2212yes—
27C2×C4×Dic15C2211yescharacteristic
28#91776C2218yescomplemented
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C5×Dic3⋊C4C2212yes—
31C5×D3×C4⋊C4C2218yes—
32C2×C3×#683C2212yes—
33C2×C3×C4×Dic5C2212yes—
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4033C2218yescomplemented
36C2×#6669C2212yes—
37C2×#6668C2212yes—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2212yes—
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2212yes—
42D3×#683C22116yes—
43C4×D3×Dic5C2218yes—
44C4×D3×Dic5C22116yes—
45#91333C2218yescomplemented
46#91331C2218yescomplemented
47#91325C22116yescomplemented
48#91323C22116yescomplemented
49C2×C4×D3×Q8—51nomaximal, Hall
50C23×Dic10—31no—
51C22×C5×C4⋊C4—31no—
52C22×#683—32no—
53C22×C4×Dic5—32no—
54C22×C4×Dic5—31no—
55C2×#4033—32no—
56C2×#4033—32no—
57C2×#4033—31no—
58C2×#4033—316no—
59C2×#4033—31no—
60C2×#4033—31no—
61C2×#4033D311yescharacteristic, direct product factor
62C23×C5×D3C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C2×Dic30C2×C418yescomplemented
69C2×Dic30C2314yes—
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2311yescharacteristic
72C2×C4×C5×D3—28no—
73C2×C4×C5×D3C2×C418yes—
74C2×C4×C5×D3C2318yes—
75C2×C4×C5×D3C2314yes—
76C22×C3×Dic5C2311yescharacteristic
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2311yescharacteristic
79C2×C3×Dic10C2×C418yescomplemented
80C2×C3×Dic10C2314yes—
81C2×#1204C2×C4116yescomplemented
82C2×#1204C2318yes—
83C2×D3×Dic5—24no—
84C2×D3×Dic5C2×C4116yes—
85C2×D3×Dic5Q818yescomplemented
86C2×D3×Dic5C2314yes—
87C2×D3×Dic5C2318yes—
88C2×D3×Dic5C2314yes—
89D3×Dic10C2×C4164yescomplemented
90C3×C5×C4⋊C4C2314yes—
91#6712C2318yes—
92C4×Dic15C2318yes—
93C4×Dic15C2314yes—
94C5×C4⋊Dic3C2314yes—
95C5×Dic3⋊C4C2318yes—
96C3×#683C2318yes—
97C3×C4×Dic5C2318yes—
98C3×C4×Dic5C2314yes—
99#6669C2318yes—
100#6668C2318yes—
101Dic3×Dic5C2314yes—
102Dic3×Dic5C2318yes—
103Dic3×Dic5C2314yes—
104Dic3×Dic5C2318yes—
105C22×D3×Q8—51no—
106C2×C3×C4×Q8—51no—
107C2×Q8×Dic3—51no—
108C4×D3×Q8—516no—
109C2×D3×C4⋊C4—52no—
110C2×D3×C4⋊C4D511yescharacteristic
111C2×#887—51no—
112C2×#887—52no—
113C2×C42×D3—52no—
114C2×C42×D3—51no—
115C2×C4×Dic6—51no—
116C2×C4×Dic6—52no—
117C23×C4×C5—31no—
118C23×C4×C5—32no—
119C23×Dic5—31no—
120C23×Dic5—32no—
121C23×Dic5—31no—
122C22×Dic10—31no—
123C22×Dic10—32no—
124C22×Dic10—316no—
125C22×Dic10—38no—
126C22×Dic10C2×D311yescharacteristic
127C2×C5×C4⋊C4—32no—
128C2×C5×C4⋊C4—31no—
129C2×C5×C4⋊C4—38no—
130C2×C5×C4⋊C4C2×D311yescharacteristic
131C2×#683—32no—
132C2×#683—32no—
133C2×#683—32no—
134C2×#683—316no—
135C2×#683C2×D312yes—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—31no—
140C2×C4×Dic5—32no—
141C2×C4×Dic5—31no—
142C2×C4×Dic5—316no—
143C2×C4×Dic5—38no—
144C2×C4×Dic5C2×D311yescharacteristic
145C2×C4×Dic5C2×D312yes—
146#4033—38no—
147#4033—38no—
148#4033—316no—
149#4033—316no—
150#4033—38no—
151#4033C2×D318yesdirect product factor
152C22×C4×Q8—151noSylow
153C23×C3×C5C2411yescharacteristic
154C22×C5×D3C22×C414yes—
155C22×C5×D3C2×Q814yes—
156C22×C5×D3#4114yes—
157C22×C5×D3C2412yes—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5C22×C414yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15C22×C418yes—
164C2×Dic15C2×Q814yescomplemented
165C2×Dic15C2412yes—
166C2×Dic15C2414yes—
167C2×Dic15C2412yes—
168Dic30C22×C4116yescomplemented
169C2×C5×Dic3—24no—
170C2×C5×Dic3C22×C414yes—
171C2×C5×Dic3C2414yes—
172C2×C5×Dic3C2412yes—
173C4×C5×D3—216no—
174C4×C5×D3C22×C4116yes—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C22×C418yes—
177C2×C3×Dic5C2×Q814yescomplemented
178C2×C3×Dic5C2412yes—
179C2×C3×Dic5C2414yes—
180C2×C3×Dic5C2412yes—
181C3×Dic10C22×C4116yescomplemented
182#1204C22×C4132yescomplemented
183D3×Dic5—28no—
184D3×Dic5C22×C4132yes—
185D3×Dic5C2×Q8116yescomplemented
186C22×C3×Q8—51no—
187C2×D3×Q8—516no—
188C2×D3×Q8—58no—
189C22×C4×D3—52no—
190C22×C4×D3—51no—
191C22×C4×D3—51no—
192C22×C4×D3C2×D512yes—
193C22×C4×D3C2×D511yescharacteristic
194C22×Dic6—51no—
195C22×Dic6—52no—
196C3×C4×Q8—58no—
197C2×C3×C4⋊C4—52no—
198C2×C3×C4⋊C4C2×D511yescharacteristic
199C2×C3×C42—52no—
200C2×C3×C42—51no—
201Q8×Dic3—58no—
202C2×C4⋊Dic3—52no—
203C2×C4⋊Dic3C2×D511yescharacteristic
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—52no—
206C2×Dic3⋊C4C2×D512yes—
207C2×C4×Dic3—52no—
208C2×C4×Dic3—51no—
209C2×C4×Dic3—52no—
210C2×C4×Dic3—51no—
211C2×C4×Dic3—51no—
212C2×C4×Dic3—52no—
213D3×C4⋊C4—516no—
214D3×C4⋊C4C2×D518yes—
215#887—58no—
216#887—516no—
217C42×D3—516no—
218C42×D3—58no—
219C4×Dic6—58no—
220C4×Dic6—516no—
221C24×C5—31no—
222C22×C4×C5—31no—
223C22×C4×C5—38no—
224C22×C4×C5—34no—
225C22×C4×C5—32no—
226C22×C4×C5—38no—
227C22×C4×C5—68no—
228C22×C4×C5C22×D312yes—
229C22×C4×C5C22×D311yescharacteristic
230C22×Dic5—32no—
231C22×Dic5—31no—
232C22×Dic5—316no—
233C22×Dic5—38no—
234C22×Dic5—38no—
235C22×Dic5—34no—
236C22×Dic5—31no—
237C22×Dic5—34no—
238C22×Dic5—64no—
239C22×Dic5C22×D311yescharacteristic
240C22×Dic5C22×D312yes—
241C22×Dic5C22×D311yescharacteristic
242C2×Dic10—38no—
243C2×Dic10—34no—
244C2×Dic10—316no—
245C2×Dic10—38no—
246C2×Dic10—364no—
247C2×Dic10C4×D318yescomplemented
248C2×Dic10C22×D314yes—
249C5×C4⋊C4—38no—
250C5×C4⋊C4—34no—
251C5×C4⋊C4C22×D314yes—
252#683—38no—
253#683—38no—
254#683—38no—
255#683C22×D318yes—
256C4×Dic5—38no—
257C4×Dic5—34no—
258C4×Dic5—34no—
259C4×Dic5—38no—
260C4×Dic5—38no—
261C4×Dic5—34no—
262C4×Dic5C22×D314yes—
263C4×Dic5C22×D318yes—
264C23×Q8—151no—
265C2×C4×Q8—51no—
266C2×C4×Q8—152no—
267C2×C4×Q8—151no—
268C2×C4×Q8—152no—
269C2×C4×Q8—1516no—
270C2×C4×Q8—151no—
271C2×C4×Q8—151no—
272C22×C4⋊C4—31no—
273C22×C4⋊C4—152no—
274C22×C42—151no—
275C22×C42—152no—
276C22×C3×C5C23×C412yes—
277C22×C3×C5C22×Q812yes—
278C22×C3×C5C2×#4112yes—
279C22×C3×C5C2511yescharacteristic
280C2×C5×D3C4×Q8116yescomplemented
281C2×C5×D3C23×C414yes—
282C2×C5×D3C22×Q814yes—
283C2×C5×D3C2×#4114yes—
284C3×C4×C5—24no—
285C3×C4×C5C23×C414yes—
286Dic15—22no—
287Dic15C23×C418yes—
288Dic15C22×Q814yescomplemented
289C3×Dic5—22no—
290C3×Dic5C23×C418yes—
291C3×Dic5C22×Q814yescomplemented
292C5×Dic3—24no—
293C5×Dic3C23×C414yes—
294C23×D3C22×D511yescharacteristic
295C2×C3×Q8—58no—
296C2×C3×Q8—54no—
297C22×C3×C4—51no—
298C22×C3×C4—52no—
299C22×C3×C4—51no—
300C22×C3×C4C22×D512yes—
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—51no—
303C22×Dic3—52no—
304C22×Dic3—51no—
305C22×Dic3C22×D512yes—
306C22×Dic3C22×D511yescharacteristic
307D3×Q8—564no—
308C2×C4×D3—28no—
309C2×C4×D3—516no—
310C2×C4×D3—58no—
311C2×C4×D3—54no—
312C2×C4×D3—58no—
313C2×C4×D3—54no—
314C2×C4×D3—104no—
315C2×C4×D3C4×D518yes—
316C2×C4×D3C22×D518yes—
317C2×C4×D3C22×D514yes—
318C2×Dic6—58no—
319C2×Dic6—54no—
320C2×Dic6—516no—
321C2×Dic6—58no—
322C3×C4⋊C4—58no—
323C3×C4⋊C4C22×D514yes—
324C3×C42—58no—
325C3×C42—54no—
326C4⋊Dic3—58no—
327C4⋊Dic3C22×D514yes—
328Dic3⋊C4—58no—
329Dic3⋊C4—58no—
330Dic3⋊C4C22×D518yes—
331C4×Dic3—58no—
332C4×Dic3—54no—
333C4×Dic3—58no—
334C4×Dic3—54no—
335C4×Dic3—54no—
336C4×Dic3—58no—
337C23×C5—34no—
338C23×C5—34no—
339C23×C5—34no—
340C23×C5—32no—
341C23×C5C23×D311yescharacteristic
342C2×C4×C5—24no—
343C2×C4×C5—34no—
344C2×C4×C5—32no—
345C2×C4×C5—316no—
346C2×C4×C5—34no—
347C2×C4×C5—616no—
348C2×C4×C5—64no—
349C2×C4×C5C2×C4×D314yes—
350C2×C4×C5C23×D314yes—
351C2×C4×C5C23×D312yes—
352C2×Dic5—22no—
353C2×Dic5—38no—
354C2×Dic5—34no—
355C2×Dic5—32no—
356C2×Dic5—34no—
357C2×Dic5—332no—
358C2×Dic5—316no—
359C2×Dic5—32no—
360C2×Dic5—68no—
361C2×Dic5—62no—
362C2×Dic5C2×C4×D318yes—
363C2×Dic5D3×Q814yescomplemented
364C2×Dic5C23×D312yes—
365C2×Dic5C23×D314yes—
366C2×Dic5C23×D312yes—
367Dic10—316no—
368Dic10—332no—
369Dic10C2×C4×D3116yescomplemented
370C22×Q8—51no—
371C22×Q8—152no—
372C22×Q8—158no—
373C22×Q8—1516no—
374C22×Q8—151no—
375C23×C4—31no—
376C23×C4—32no—
377C23×C4—152no—
378C23×C4—151no—
379C23×C4—151no—
380C4×Q8—58no—
381C4×Q8—1516no—
382C4×Q8—158no—
383C4×Q8—1516no—
384C4×Q8—158no—
385C4×Q8—158no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—38no—
389C2×C4⋊C4—52no—
390C2×C4⋊C4—1516no—
391C2×C4⋊C4—152no—
392C2×C4⋊C4—152no—
393C2×C4⋊C4—152no—
394C2×C4⋊C4D3×D511yescharacteristic
395C2×C42—52no—
396C2×C42—51no—
397C2×C42—158no—
398C2×C42—1516no—
399C2×C42—151no—
400C2×C42—151no—
401C2×C42—152no—
402C2×C42—152no—
403C2×C42—152no—
404C2×C42—151no—
405C2×C3×C5C2×C4×Q814yescomplemented
406C2×C3×C5C24×C411yescharacteristic
407C2×C3×C5C23×Q811yescharacteristic
408C2×C3×C5C22×#4111yescharacteristic
409C5×D3C2×C4×Q818yescomplemented
410C23×C3C23×D511yescharacteristic
411C22×D3C2×C4×D514yes—
412C22×D3#71114yes—
413C22×D3Q8×D514yes—
414C22×D3C23×D512yes—
415C3×Q8—516no—
416C2×C3×C4—24no—
417C2×C3×C4—58no—
418C2×C3×C4—54no—
419C2×C3×C4—52no—
420C2×C3×C4—54no—
421C2×C3×C4—52no—
422C2×C3×C4—102no—
423C2×C3×C4C2×C4×D514yes—
424C2×C3×C4C23×D514yes—
425C2×C3×C4C23×D512yes—
426C2×Dic3—24no—
427C2×Dic3—58no—
428C2×Dic3—54no—
429C2×Dic3—52no—
430C2×Dic3—54no—
431C2×Dic3—52no—
432C2×Dic3—102no—
433C2×Dic3C2×C4×D514yes—
434C2×Dic3C23×D514yes—
435C2×Dic3C23×D512yes—
436C4×D3—216no—
437C4×D3—532no—
438C4×D3—516no—
439C4×D3—108no—
440C4×D3C2×C4×D5116yes—
441Dic6—516no—
442Dic6—532no—
443C22×C5—34no—
444C22×C5—34no—
445C22×C5—34no—
446C22×C5—316no—
447C22×C5C22×C4×D312yes—
448C22×C5C2×D3×Q812yes—
449C22×C5D3×#4112yes—
450C22×C5C24×D311yescharacteristic
451C4×C5—24no—
452C4×C5—34no—
453C4×C5—64no—
454C4×C5C22×C4×D314yes—
455Dic5—22no—
456Dic5—38no—
457Dic5—34no—
458Dic5—62no—
459Dic5C22×C4×D318yes—
460Dic5C2×D3×Q814yescomplemented
461C24—31no—
462C2×Q8—58no—
463C2×Q8—54no—
464C2×Q8—158no—
465C2×Q8—1516no—
466C2×Q8—1564no—
467C2×Q8—158no—
468C2×Q8—154no—
469C22×C4—31no—
470C22×C4—38no—
471C22×C4—34no—
472C22×C4—32no—
473C22×C4—38no—
474C22×C4—51no—
475C22×C4—52no—
476C22×C4—51no—
477C22×C4—68no—
478C22×C4—154no—
479C22×C4—158no—
480C22×C4—1516no—
481C22×C4—158no—
482C22×C4—154no—
483C22×C4—151no—
484C22×C4—152no—
485C22×C4—151no—
486C22×C4—304no—
487C22×C4C2×D3×D512yes—
488C22×C4C2×D3×D511yescharacteristic
489C4⋊C4—38no—
490C4⋊C4—34no—
491C4⋊C4—58no—
492C4⋊C4—158no—
493C4⋊C4—158no—
494C4⋊C4—158no—
495C4⋊C4C2×D3×D514yes—
496C42—58no—
497C42—54no—
498C42—154no—
499C42—154no—
500C42—158no—
501C42—158no—
502C42—158no—
503C42—154no—
504C3×C5C22×C4×Q811yescharacteristic, complemented, Hall
505C22×C3C22×C4×D512yes—
506C22×C3C2×#71112yes—
507C22×C3C2×Q8×D512yes—
508C22×C3C24×D511yescharacteristic
509C2×D3#4033116yesdirect product factor
510C2×D3C22×C4×D514yes—
511C2×D3C2×#71114yes—
512C2×D3C2×Q8×D514yes—
513C3×C4—24no—
514C3×C4—58no—
515C3×C4—54no—
516C3×C4—102no—
517C3×C4C22×C4×D514yes—
518Dic3—24no—
519Dic3—58no—
520Dic3—54no—
521Dic3—102no—
522Dic3C22×C4×D514yes—
523C2×C5—38no—
524C2×C5C4×D3×Q814yescomplemented
525C2×C5C23×C4×D311yescharacteristic
526C2×C5C22×D3×Q811yescharacteristic
527C2×C5C2×D3×#4111yescharacteristic
528C23—34no—
529C23—34no—
530C23—34no—
531C23—32no—
532C23C22×D3×D511yescharacteristic
533Q8—516no—
534Q8—1532no—
535Q8—1516no—
536C2×C4—24no—
537C2×C4—34no—
538C2×C4—32no—
539C2×C4—316no—
540C2×C4—34no—
541C2×C4—58no—
542C2×C4—54no—
543C2×C4—52no—
544C2×C4—54no—
545C2×C4—52no—
546C2×C4—616no—
547C2×C4—64no—
548C2×C4—102no—
549C2×C4—1532no—
550C2×C4—1516no—
551C2×C4—158no—
552C2×C4—154no—
553C2×C4—152no—
554C2×C4—154no—
555C2×C4—152no—
556C2×C4—308no—
557C2×C4—302no—
558C2×C4C4×D3×D514yes—
559C2×C4C22×D3×D514yes—
560C2×C4C22×D3×D512yes—
561C2×C3C2×#403314yescomplemented
562C2×C3C23×C4×D511yescharacteristic
563C2×C3C22×#71111yescharacteristic
564C2×C3C22×Q8×D511yescharacteristic
565D3C2×#403318yesdirect product factor
566C5C2×C4×D3×Q811yescharacteristic, complemented, Sylow
567C22—316no—
568C22—34no—
569C22—34no—
570C22—34no—
571C22C2×C4×D3×D512yes—
572C22D3×#71112yes—
573C22D3×Q8×D512yes—
574C22C23×D3×D511yescharacteristic
575C4—24no—
576C4—34no—
577C4—58no—
578C4—54no—
579C4—64no—
580C4—102no—
581C4—158no—
582C4—154no—
583C4—302no—
584C4C2×C4×D3×D514yes—
585C3C22×#403311yescharacteristic, complemented, Sylow
586C2—38no—
587C2D3×#403314yesdirect product factor
588C2C22×C4×D3×D511yescharacteristic
589C2C2×D3×#71111yescharacteristic
590C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
cosocleC22×C3×C5C25
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C22×C4×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91776C2semidirect
4. C2×C3×#4033C2semidirect
8. C2×#91333C2semidirect
9. C2×#91331C2semidirect
10. C2×#91325C2semidirect
11. C2×#91323C2semidirect
12. D3×#4033C2direct (N × H)
22. C2×D3×Dic10C4semidirect
28. #91776C22semidirect
35. C3×#4033C22semidirect
45. #91333C22semidirect
46. #91331C22semidirect
47. #91325C22semidirect
48. #91323C22semidirect
61. C2×#4033D3direct (N × H)
68. C2×Dic30C2×C4semidirect
79. C2×C3×Dic10C2×C4semidirect
81. C2×#1204C2×C4semidirect
85. C2×D3×Dic5Q8semidirect
89. D3×Dic10C2×C4semidirect
151. #4033C2×D3direct (N × H)
164. C2×Dic15C2×Q8semidirect
168. Dic30C22×C4semidirect
177. C2×C3×Dic5C2×Q8semidirect
181. C3×Dic10C22×C4semidirect
182. #1204C22×C4semidirect
185. D3×Dic5C2×Q8semidirect
247. C2×Dic10C4×D3semidirect
280. C2×C5×D3C4×Q8semidirect
288. Dic15C22×Q8semidirect
291. C3×Dic5C22×Q8semidirect
363. C2×Dic5D3×Q8semidirect
369. Dic10C2×C4×D3semidirect
405. C2×C3×C5C2×C4×Q8semidirect
409. C5×D3C2×C4×Q8semidirect
460. Dic5C2×D3×Q8semidirect
504. C3×C5C22×C4×Q8semidirect
509. C2×D3#4033direct (N × H)
524. C2×C5C4×D3×Q8semidirect
561. C2×C3C2×#4033semidirect
565. D3C2×#4033direct (N × H)
566. C5C2×C4×D3×Q8semidirect
585. C3C22×#4033semidirect
587. C2D3×#4033direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic102
C2×#917762
C2×C5×D3×C4⋊C42
C2×C3×#40332
C2×D3×#6832
C2×C4×D3×Dic52
C2×#913332
C2×#913312
C2×#913252
C2×#913232
D3×#40332
C22×#40333
C2×C4×D3×Q85