Subgroups — #807

Order 96.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#107	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	—	2	1	no	—
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×Dic₃	—	2	1	no	—
8	C₃⋊C₈	C₄	1	2	yes	complemented
9	C₂×C₈	—	3	1	no	—
10	C₄⋊C₄	—	3	1	no	—
11	C₄⋊C₄	D₃	1	1	yes	characteristic
12	C₂²×C₃	D₄	1	1	yes	characteristic
13	C₃×C₄	—	4	1	no	—
14	C₃×C₄	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄	Q₈	1	1	yes	characteristic
16	Dic₃	—	4	1	no	—
17	C₂×C₄	—	2	1	no	—
18	C₂×C₄	—	6	1	no	—
19	C₂×C₄	C₂×D₃	1	1	yes	characteristic
20	C₈	—	3	2	no	—
21	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₃	D₈	1	1	yes	characteristic
23	C₂×C₃	Q₁₆	1	1	yes	characteristic
24	C₂²	#67	1	1	yes	characteristic
25	C₄	—	4	1	no	—
26	C₄	—	12	1	no	—
27	C₄	Dic₆	1	1	yes	characteristic
28	C₄	C₄×D₃	1	1	yes	characteristic
29	C₃	#107	1	1	yes	characteristic, complemented, Sylow
30	C₂	Dic₃⋊C₄	1	1	yes	characteristic
31	C₂	#213	1	1	yes	characteristic
32	C₂	#216	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₃⋊C₈	C₄	semidirect
29. C₃	#107	semidirect

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