Subgroups — #4626

Order 192.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#127⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#353	—	3	1	no	maximal, Sylow
3	SL(2,ℤ/4)	—	4	1	no	maximal
4	C₄²⋊C₃	C₄	1	1	yes	characteristic, complemented
5	#127	D₃	1	1	yes	characteristic
6	#99	—	3	1	no	—
7	#99	—	3	1	no	—
8	C₂×A₄	—	4	1	no	—
9	C₂×D₄	—	3	1	no	—
10	C₂×D₄	—	3	1	no	—
11	C₂²⋊C₄	—	6	1	no	—
12	C₂²⋊C₄	—	6	1	no	—
13	C₄²	Dic₃	1	1	yes	characteristic, complemented
14	A₄	—	4	1	no	—
15	Dic₃	—	16	1	no	—
16	C₂³	—	3	1	no	—
17	C₂³	S₄	1	1	yes	characteristic
18	D₄	—	12	1	no	—
19	D₄	—	12	1	no	—
20	C₂×C₄	—	3	1	no	—
21	C₂×C₄	—	12	1	no	—
22	C₂×C₄	—	12	1	no	—
23	C₂×C₃	—	16	1	no	—
24	C₂²	—	6	1	no	—
25	C₂²	—	6	1	no	—
26	C₂²	—	12	1	no	—
27	C₂²	SL(2,ℤ/4)	1	1	yes	characteristic
28	C₄	—	6	1	no	—
29	C₄	—	24	1	no	—
30	C₄	—	24	1	no	—
31	C₃	—	16	1	no	Sylow
32	C₂	—	3	1	no	—
33	C₂	—	4	1	no	—
34	C₂	—	12	1	no	—

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

N	H ≅ G/N	type
4. C₄²⋊C₃	C₄	semidirect
13. C₄²	Dic₃	semidirect

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