Subgroups — #874

Order 96.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂	C₂	1	6	yes	maximal, complemented
2	C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	#127	—	3	1	no	maximal, Sylow
4	C₂²×D₃	C₂²	1	4	yes	—
5	C₂×C₃×C₄	C₂²	1	3	yes	—
6	D₁₂	—	2	12	no	—
7	C₂×D₄	—	3	6	no	—
8	C₄²	D₃	1	1	yes	characteristic, complemented
9	C₂²×C₃	C₂³	1	1	yes	characteristic
10	C₂×D₃	—	2	12	no	—
11	C₃×C₄	D₄	1	6	yes	complemented
12	C₂³	—	3	4	no	—
13	D₄	—	6	12	no	—
14	C₂×C₄	C₂×D₃	1	3	yes	—
15	C₂×C₃	C₂×D₄	1	3	yes	—
16	D₃	—	4	4	no	—
17	C₂²	—	6	12	no	—
18	C₂²	C₂²×D₃	1	1	yes	characteristic
19	C₄	D₁₂	1	6	yes	complemented
20	C₃	#127	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	12	4	no	—
22	C₂	C₂×D₁₂	1	3	yes	—

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.