Subgroups — #822

Order 96.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#108	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₃×C₈	—	2	1	no	—
7	C₃⋊C₈	—	2	1	no	—
8	C₃⋊C₈	C₄	1	2	yes	—
9	M₁₆	—	3	1	no	—
10	M₁₆	D₃	1	1	yes	characteristic
11	C₂×C₈	—	3	1	no	—
12	C₂²×C₃	Q₈	1	1	yes	characteristic
13	C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄	D₄	1	1	yes	characteristic
15	C₂×C₄	C₂×D₃	1	1	yes	characteristic
16	C₈	—	2	1	no	—
17	C₈	—	3	2	no	—
18	C₈	—	6	1	no	—
19	C₂×C₃	—	2	1	no	—
20	C₂×C₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂²	Dic₆	1	1	yes	characteristic
22	C₄	C₄×D₃	1	1	yes	characteristic
23	C₄	#67	1	1	yes	characteristic
24	C₃	#108	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	2	1	no	—
26	C₂	Dic₃⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₃	#108	semidirect

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