Subgroups — #926

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	#217	C₂	1	2	yes	maximal
3	C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
4	C₄×Dic₃	C₂	1	2	yes	maximal, complemented
5	#117	—	3	1	no	maximal, Sylow
6	C₂³×C₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄	C₄	1	4	yes	complemented
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₃	C₂²	1	4	yes	—
11	C₂²×C₄	D₃	1	1	yes	characteristic
12	C₄⋊C₄	—	3	2	no	—
13	C₂²⋊C₄	—	3	2	no	—
14	C₄²	—	3	2	no	—
15	C₂²×C₃	—	2	2	no	—
16	C₂²×C₃	C₂×C₄	1	2	yes	—
17	C₂²×C₃	C₂³	1	1	yes	characteristic
18	C₃×C₄	C₂×C₄	1	2	yes	—
19	C₃×C₄	C₂×C₄	1	2	yes	—
20	Dic₃	—	2	4	no	—
21	C₂³	C₂×D₃	1	1	yes	characteristic
22	C₂×C₄	—	3	4	no	—
23	C₂×C₄	Dic₃	1	4	yes	complemented
24	C₂×C₄	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄	C₂×D₃	1	1	yes	characteristic
26	C₂×C₃	—	2	2	no	—
27	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₃	#41	1	2	yes	—
29	C₂²	—	2	2	no	—
30	C₂²	C₂×Dic₃	1	2	yes	—
31	C₂²	C₂²×D₃	1	1	yes	characteristic
32	C₄	—	6	4	no	—
33	C₄	C₂×Dic₃	1	2	yes	—
34	C₄	C₂×Dic₃	1	2	yes	—
35	C₃	#117	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	2	2	no	—
37	C₂	#235	1	2	yes	—
38	C₂	C₂²×Dic₃	1	1	yes	characteristic

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

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