Subgroups — C₂×#20259998 #27136387

Order 12352.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259998	C₂	1	2	yes	maximal, direct product factor
2	C₂×#15690567	C₂	1	1	yes	maximal, characteristic
3	#15690567	C₄	1	1	yes	characteristic
4	#15690567	C₂²	1	1	yes	characteristic
5	C₂×#13095400	C₄	1	1	yes	characteristic
6	#13095400	C₈	1	1	yes	characteristic
7	#13095400	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₉₃	C₈	1	1	yes	characteristic
9	C₂²×C₁₉₃	C₁₆	1	1	yes	characteristic
10	Dic₁₉₃	C₁₆	1	1	yes	characteristic
11	Dic₁₉₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₉₃	C₃₂	1	2	yes	complemented
13	C₂×C₁₉₃	C₂×C₁₆	1	1	yes	characteristic
14	C₁₉₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	193	1	no	maximal, Sylow
16	C₂×C₁₆	—	193	1	no	—
17	C₃₂	—	193	2	no	—
18	C₂×C₈	—	193	1	no	—
19	C₁₆	—	193	1	no	—
20	C₁₆	—	193	1	no	—
21	C₂×C₄	—	193	1	no	—
22	C₈	—	193	1	no	—
23	C₈	—	193	1	no	—
24	C₂²	#15690569	1	1	yes	characteristic
25	C₄	—	193	1	no	—
26	C₄	—	193	1	no	—
27	C₂	#20259998	1	2	yes	direct product factor
28	C₂	C₂×#15690569	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.