Subgroups — #833

Order 96.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	#208	C₂	1	2	yes	maximal, complemented
3	#100	—	3	1	no	maximal, Sylow
4	C₂³×C₃	C₄	1	2	yes	—
5	C₃×D₄	—	2	2	no	—
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊C₈	—	2	2	no	—
8	C₂×D₄	D₃	1	1	yes	characteristic
9	M₁₆	—	3	2	no	—
10	C₂²×C₃	—	2	2	no	—
11	C₂²×C₃	—	4	2	no	—
12	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄	D₄	1	2	yes	—
14	C₂³	Dic₃	1	2	yes	—
15	D₄	—	2	2	no	—
16	C₂×C₄	C₂×D₃	1	1	yes	characteristic
17	C₈	—	6	2	no	—
18	C₂×C₃	—	2	1	no	—
19	C₂×C₃	—	4	2	no	—
20	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂²	—	2	2	no	—
22	C₂²	—	4	2	no	—
23	C₂²	C₂×Dic₃	1	1	yes	characteristic
24	C₄	#67	1	2	yes	—
25	C₃	#100	1	1	yes	characteristic, complemented, Sylow
26	C₂	—	2	1	no	—
27	C₂	—	4	2	no	—
28	C₂	#217	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #208	C₂	semidirect
25. C₃	#100	semidirect

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