Subgroups — #816

Order 96.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	#103	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×Dic₃	—	2	1	no	—
7	C₂×Dic₃	—	2	1	no	—
8	Dic₆	—	2	1	no	—
9	Dic₆	C₄	1	2	yes	complemented
10	C₃×C₈	—	2	1	no	—
11	C₂×Q₈	—	3	1	no	—
12	C₂×C₈	D₃	1	1	yes	characteristic
13	C₄⋊C₄	—	3	1	no	—
14	C₂²×C₃	D₄	1	1	yes	characteristic
15	C₃×C₄	C₂×C₄	1	1	yes	characteristic
16	C₃×C₄	D₄	1	1	yes	characteristic
17	Dic₃	—	2	2	no	—
18	Dic₃	—	4	1	no	—
19	Q₈	—	3	2	no	—
20	Q₈	—	6	1	no	—
21	C₂×C₄	—	6	1	no	—
22	C₂×C₄	—	6	1	no	—
23	C₂×C₄	C₂×D₃	1	1	yes	characteristic
24	C₈	—	2	1	no	—
25	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₃	SD₁₆	1	1	yes	characteristic
27	C₂×C₃	Q₁₆	1	1	yes	characteristic
28	C₂²	D₁₂	1	1	yes	characteristic
29	C₄	—	6	2	no	—
30	C₄	—	12	1	no	—
31	C₄	C₄×D₃	1	1	yes	characteristic
32	C₄	#67	1	1	yes	characteristic
33	C₃	#103	1	1	yes	characteristic, complemented, Sylow
34	C₂	#204	1	1	yes	characteristic
35	C₂	Dic₁₂	1	1	yes	characteristic
36	C₂	(C₂×D₃)⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
9. Dic₆	C₄	semidirect
33. C₃	#103	semidirect

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