Subgroups — #836

Order 96.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	#208	C₂	1	2	yes	maximal
3	#101	—	3	1	no	maximal, Sylow
4	C₃×Q₈	—	2	2	no	—
5	C₂×C₃×C₄	C₄	1	2	yes	—
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊C₈	—	2	2	no	—
8	C₂×Q₈	D₃	1	1	yes	characteristic
9	M₁₆	—	3	2	no	—
10	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄	—	2	2	no	—
12	C₃×C₄	D₄	1	2	yes	—
13	Q₈	—	2	2	no	—
14	C₂×C₄	Dic₃	1	2	yes	—
15	C₂×C₄	C₂×D₃	1	1	yes	characteristic
16	C₈	—	6	2	no	—
17	C₂×C₃	—	2	1	no	—
18	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂²	C₂×Dic₃	1	1	yes	characteristic
20	C₄	—	2	2	no	—
21	C₄	#67	1	2	yes	—
22	C₃	#101	1	1	yes	characteristic, complemented, Sylow
23	C₂	—	2	1	no	—
24	C₂	#217	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₃	#101	semidirect

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