Finite Group Databasebeta

← C3×#23919 #10642526

Subgroups — C3×#23919 #10642526

Order 768.

2252 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C3×#121C211yesmaximal, characteristic
3C2×C3×#448C212yesmaximal, complemented
4C2×C3×#450C212yesmaximal, complemented
5C3×#2000C214yesmaximal, complemented
6C3×#1874C212yesmaximal, complemented
7C3×#1872C212yesmaximal, complemented
8C3×#1779C211yesmaximal, characteristic, complemented
9#23919C311yesmaximal, characteristic, direct product factor, Sylow
10C23×C3×Q8C2211yescharacteristic, complemented
11C23×C3×D4—21no—
12C23×C3×D4C2211yescharacteristic
13C24×C3×C4C2211yescharacteristic
14C22×C3×SD16C2214yescomplemented
15C2×C3×C22⋊Q8—21no—
16C2×C3×C22⋊Q8—21no—
17C2×C3×C22⋊Q8—28no—
18C2×C3×C22⋊Q8C2212yes—
19C2×C3×C22⋊Q8C2212yescomplemented
20C2×C3×#121—21no—
21C2×C3×#121—21no—
22C2×C3×#121—28no—
23C2×C3×#121C2212yes—
24C2×C3×#121C2212yes—
25C22×C3×C4⋊C4—21no—
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic, complemented
28C22×C3×C22⋊C4—21no—
29C22×C3×C22⋊C4—21no—
30C3×#450—28no—
31C3×#448—28no—
32C2×C3×#103C2214yescomplemented
33C2×C3×#102C2214yescomplemented
34C2×C3×C22⋊C8C2212yes—
35C2×C3×C22⋊C8C2212yescomplemented
36C2×C3×C22⋊C8C2212yescomplemented
37C3×#340C2214yescomplemented
38C22×C22⋊Q8C2×C311yescharacteristic, complemented
39C22×#121C2×C311yescharacteristic
40C2×#448C2×C312yescomplemented
41C2×#450C2×C312yescomplemented
42#2000C2×C314yescomplemented
43#1874C2×C312yescomplemented
44#1872C2×C312yescomplemented
45#1779C2×C311yescharacteristic, complemented
46C25×C3—21no—
47C25×C3D411yescharacteristic
48C22×C3×Q8—24no—
49C22×C3×Q8—21no—
50C22×C3×Q8—24no—
51C22×C3×Q8—42no—
52C22×C3×Q8C2312yes—
53C22×C3×D4—28no—
54C22×C3×D4—22no—
55C22×C3×D4—22no—
56C22×C3×D4—24no—
57C22×C3×D4—21no—
58C22×C3×D4—24no—
59C22×C3×D4—42no—
60C22×C3×D4—44no—
61C22×C3×D4—44no—
62C22×C3×D4C2312yes—
63C23×C3×C4—21no—
64C23×C3×C4—21no—
65C23×C3×C4—21no—
66C23×C3×C4—24no—
67C23×C3×C4—24no—
68C23×C3×C4—42no—
69C23×C3×C4D411yescharacteristic
70C23×C3×C4D411yescharacteristic
71C23×C3×C4D411yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C2×C3×SD16—28no—
76C2×C3×SD16—28no—
77C2×C3×SD16—44no—
78C22×C3×C8C2314yes—
79C3×C22⋊Q8—28no—
80C3×C22⋊Q8—28no—
81C3×C22⋊Q8—24no—
82C3×C22⋊Q8—24no—
83C3×C22⋊Q8—24no—
84C3×C22⋊Q8D418yescomplemented
85C3×#121—28no—
86C3×#121—28no—
87C3×#121—24no—
88C3×#121—24no—
89C3×#121—24no—
90C3×#121D418yes—
91C2×C3×C4⋊C4—28no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—24no—
97C2×C3×C4⋊C4—24no—
98C2×C3×C4⋊C4C2312yes—
99C2×C3×C4⋊C4C2312yes—
100C2×C3×C22⋊C4—28no—
101C2×C3×C22⋊C4—28no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C3×#103—28no—
107C3×#102—28no—
108C3×C22⋊C8—24no—
109C3×C22⋊C8—24no—
110C3×C22⋊C8—42no—
111C23×Q8C22×C311yescharacteristic, complemented
112C23×D4—21no—
113C23×D4C22×C311yescharacteristic
114C24×C4C22×C311yescharacteristic
115C22×SD16C22×C314yescomplemented
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8C22×C312yes—
120C2×C22⋊Q8C22×C312yescomplemented
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—28no—
124C2×#121C22×C312yes—
125C2×#121C22×C312yes—
126C22×C4⋊C4—21no—
127C22×C4⋊C4C22×C311yescharacteristic
128C22×C4⋊C4C22×C311yescharacteristic, complemented
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131#450—28no—
132#448—28no—
133C2×#103C22×C314yescomplemented
134C2×#102C22×C314yescomplemented
135C2×C22⋊C8C22×C312yes—
136C2×C22⋊C8C22×C312yescomplemented
137C2×C22⋊C8C22×C312yescomplemented
138#340C22×C314yescomplemented
139C24×C3—22no—
140C24×C3—22no—
141C24×C3—22no—
142C24×C3—22no—
143C24×C3—24no—
144C24×C3—22no—
145C24×C3—41no—
146C24×C3—41no—
147C24×C3—42no—
148C24×C3—42no—
149C24×C3—42no—
150C24×C3—42no—
151C24×C3—42no—
152C24×C3—42no—
153C24×C3SD1614yescomplemented
154C24×C3C2×D411yescharacteristic
155C24×C3C2×D411yescharacteristic
156C24×C3C2×D411yescharacteristic
157C2×C3×Q8—24no—
158C2×C3×Q8—22no—
159C2×C3×Q8—24no—
160C2×C3×Q8—24no—
161C2×C3×Q8—416no—
162C2×C3×Q8—42no—
163C2×C3×Q8—42no—
164C2×C3×Q8C2×D414yescomplemented
165C2×C3×D4—24no—
166C2×C3×D4—28no—
167C2×C3×D4—28no—
168C2×C3×D4—24no—
169C2×C3×D4—22no—
170C2×C3×D4—24no—
171C2×C3×D4—416no—
172C2×C3×D4—42no—
173C2×C3×D4—432no—
174C2×C3×D4—44no—
175C2×C3×D4—44no—
176C2×C3×D4—44no—
177C2×C3×D4—44no—
178C2×C3×D4—42no—
179C2×C3×D4C2×D414yes—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—24no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—416no—
203C22×C3×C4—42no—
204C22×C3×C4—42no—
205C22×C3×C4—42no—
206C22×C3×C4—42no—
207C22×C3×C4—42no—
208C22×C3×C4—42no—
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4C2×D414yes—
213C22×C3×C4C2×D414yes—
214C22×C3×C4C2411yescharacteristic
215C3×SD16—416no—
216C2×C3×C8—24no—
217C2×C3×C8—24no—
218C2×C3×C8—24no—
219C3×C4⋊C4—24no—
220C3×C4⋊C4—24no—
221C3×C4⋊C4—28no—
222C3×C4⋊C4—28no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4C2×D414yes—
226C3×C4⋊C4C2×D414yescomplemented
227C3×C22⋊C4—28no—
228C3×C22⋊C4—28no—
229C3×C22⋊C4—28no—
230C3×C22⋊C4—28no—
231C25—21no—
232C25C3×D411yescharacteristic
233C22×Q8—24no—
234C22×Q8—21no—
235C22×Q8—24no—
236C22×Q8—42no—
237C22×Q8C23×C312yes—
238C22×D4—28no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—21no—
243C22×D4—24no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4C23×C312yes—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—42no—
254C23×C4C3×D411yescharacteristic
255C23×C4C3×D411yescharacteristic
256C23×C4C3×D411yescharacteristic
257C23×C4C23×C311yescharacteristic
258C23×C4C23×C311yescharacteristic
259C23×C4C23×C311yescharacteristic
260C2×SD16—28no—
261C2×SD16—28no—
262C2×SD16—44no—
263C22×C8C23×C314yes—
264C22⋊Q8—28no—
265C22⋊Q8—28no—
266C22⋊Q8—24no—
267C22⋊Q8—24no—
268C22⋊Q8—24no—
269C22⋊Q8C3×D418yescomplemented
270#121—28no—
271#121—28no—
272#121—24no—
273#121—24no—
274#121—24no—
275#121C3×D418yes—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4C23×C312yes—
284C2×C4⋊C4C23×C312yes—
285C2×C22⋊C4—28no—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291#103—28no—
292#102—28no—
293C22⋊C8—24no—
294C22⋊C8—24no—
295C22⋊C8—42no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—28no—
311C23×C3—28no—
312C23×C3—24no—
313C23×C3—44no—
314C23×C3—44no—
315C23×C3—44no—
316C23×C3—44no—
317C23×C3—44no—
318C23×C3—48no—
319C23×C3—48no—
320C23×C3—48no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—84no—
328C23×C3—84no—
329C23×C3—84no—
330C23×C3—84no—
331C23×C3#12012yes—
332C23×C3#12012yes—
333C23×C3C2×SD1612yes—
334C23×C3C2×SD1612yes—
335C23×C3C2×SD1612yes—
336C23×C3AGL(1,ℤ/8)12yes—
337C23×C3#13712yes—
338C23×C3C22×D411yescharacteristic
339C3×Q8—28no—
340C3×Q8—48no—
341C3×Q8—44no—
342C3×D4—28no—
343C3×D4—48no—
344C3×D4—416no—
345C3×D4—416no—
346C3×D4—44no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—28no—
352C2×C3×C4—28no—
353C2×C3×C4—21no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—44no—
360C2×C3×C4—44no—
361C2×C3×C4—44no—
362C2×C3×C4—48no—
363C2×C3×C4—48no—
364C2×C3×C4—48no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—44no—
372C2×C3×C4#12012yes—
373C2×C3×C4#12012yes—
374C2×C3×C4C22×D412yes—
375C2×C3×C4C22×D412yes—
376C2×C3×C4H(5,𝔽2)12yes—
377C3×C8—44no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—24no—
383C24—22no—
384C24—41no—
385C24—41no—
386C24—42no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24C3×SD1614yescomplemented
393C24C2×C3×D411yescharacteristic
394C24C2×C3×D411yescharacteristic
395C24C2×C3×D411yescharacteristic
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—416no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8C2×C3×D414yescomplemented
404C2×D4—24no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—416no—
411C2×D4—42no—
412C2×D4—432no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—42no—
418C2×D4C2×C3×D414yes—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—416no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4C2×C3×D411yescharacteristic
449C22×C4C2×C3×D411yescharacteristic
450C22×C4C2×C3×D411yescharacteristic
451C22×C4C2×C3×D414yes—
452C22×C4C2×C3×D414yes—
453C22×C4C24×C311yescharacteristic
454SD16—416no—
455C2×C8—24no—
456C2×C8—24no—
457C2×C8—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C2×C3×D414yes—
465C4⋊C4C2×C3×D414yescomplemented
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—416no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—44no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—816no—
494C22×C3—82no—
495C22×C3—82no—
496C22×C3—82no—
497C22×C3—82no—
498C22×C3#44814yescomplemented
499C22×C3#45014yescomplemented
500C22×C3C2×#12011yescharacteristic
501C22×C3C2×#12011yescharacteristic
502C22×C3#53411yescharacteristic
503C22×C3C22×SD1611yescharacteristic
504C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
505C22×C3C2×#13711yescharacteristic
506C22×C3#57511yescharacteristic
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—41no—
510C3×C4—44no—
511C3×C4—44no—
512C3×C4—44no—
513C3×C4D4214yes—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—28no—
526C23—28no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—24no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—44no—
535C23—44no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—84no—
546C23—84no—
547C23—84no—
548C23—84no—
549C23C3×#12012yes—
550C23C3×#12012yes—
551C23C2×C3×SD1612yes—
552C23C2×C3×SD1612yes—
553C23C2×C3×SD1612yes—
554C23C3×AGL(1,ℤ/8)12yes—
555C23C3×#13712yes—
556C23C22×C3×D411yescharacteristic
557Q8—28no—
558Q8—48no—
559Q8—44no—
560D4—28no—
561D4—48no—
562D4—416no—
563D4—416no—
564D4—44no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—21no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—48no—
581C2×C4—48no—
582C2×C4—48no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—44no—
590C2×C4C3×#12012yes—
591C2×C4C3×#12012yes—
592C2×C4C22×C3×D412yes—
593C2×C4C22×C3×D412yes—
594C2×C4C3×H(5,𝔽2)12yes—
595C8—44no—
596C2×C3—24no—
597C2×C3—24no—
598C2×C3—42no—
599C2×C3—84no—
600C2×C3#240311yescharacteristic
601C2×C3C2×#45011yescharacteristic
602C2×C3C2×#44811yescharacteristic
603C2×C3#300611yescharacteristic
604C2×C3#300711yescharacteristic
605C2×C3#318711yescharacteristic
606C2×C3#319311yescharacteristic
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—416no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—44no—
628C22—44no—
629C22—44no—
630C22—816no—
631C22—82no—
632C22—82no—
633C22—82no—
634C22—82no—
635C22C3×#44814yescomplemented
636C22C3×#45014yescomplemented
637C22C2×C3×#12011yescharacteristic
638C22C2×C3×#12011yescharacteristic
639C22C3×#53411yescharacteristic
640C22C22×C3×SD1611yescharacteristic
641C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
642C22C2×C3×#13711yescharacteristic
643C22C3×#57511yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—44no—
648C4—44no—
649C4—44no—
650C4C3×D4214yes—
651C3#2391911yescharacteristic, direct product factor, Sylow
652C2—24no—
653C2—24no—
654C2—42no—
655C2—84no—
656C2C3×#240311yescharacteristic
657C2C2×C3×#45011yescharacteristic
658C2C2×C3×#44811yescharacteristic
659C2C3×#300611yescharacteristic
660C2C3×#300711yescharacteristic
661C2C3×#318711yescharacteristic
662C2C3×#319311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
3. C2×C3×#448C2semidirect
4. C2×C3×#450C2semidirect
5. C3×#2000C2semidirect
6. C3×#1874C2semidirect
7. C3×#1872C2semidirect
8. C3×#1779C2semidirect
9. #23919C3direct (N × H)
10. C23×C3×Q8C22semidirect
14. C22×C3×SD16C22semidirect
19. C2×C3×C22⋊Q8C22semidirect
27. C22×C3×C4⋊C4C22semidirect
32. C2×C3×#103C22semidirect
33. C2×C3×#102C22semidirect
35. C2×C3×C22⋊C8C22semidirect
36. C2×C3×C22⋊C8C22semidirect
37. C3×#340C22semidirect
38. C22×C22⋊Q8C2×C3semidirect
40. C2×#448C2×C3semidirect
41. C2×#450C2×C3semidirect
42. #2000C2×C3semidirect
43. #1874C2×C3semidirect
44. #1872C2×C3semidirect
45. #1779C2×C3semidirect
84. C3×C22⋊Q8D4semidirect
111. C23×Q8C22×C3semidirect
115. C22×SD16C22×C3semidirect
120. C2×C22⋊Q8C22×C3semidirect
128. C22×C4⋊C4C22×C3semidirect
133. C2×#103C22×C3semidirect
134. C2×#102C22×C3semidirect
136. C2×C22⋊C8C22×C3semidirect
137. C2×C22⋊C8C22×C3semidirect
138. #340C22×C3semidirect
153. C24×C3SD16semidirect
164. C2×C3×Q8C2×D4semidirect
226. C3×C4⋊C4C2×D4semidirect
269. C22⋊Q8C3×D4semidirect
392. C24C3×SD16semidirect
403. C2×Q8C2×C3×D4semidirect
465. C4⋊C4C2×C3×D4semidirect
498. C22×C3#448semidirect
499. C22×C3#450semidirect
635. C22C3×#448semidirect
636. C22C3×#450semidirect
651. C3#23919direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×C3×#1212
C2×C3×#4482
C2×C3×#4502
C3×#20002
C3×#18742
C3×#18722
C3×#17792
#239193