Subgroups — C₂×#26013689 #36375074

Order 22336.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26013689	C₂	1	2	yes	maximal, direct product factor
2	C₂×#19150208	C₂	1	1	yes	maximal, characteristic
3	#19150208	C₄	1	1	yes	characteristic
4	#19150208	C₂²	1	1	yes	characteristic
5	C₂×C₈×C₃₄₉	C₄	1	1	yes	characteristic
6	C₂×C₄×C₃₄₉	C₈	1	1	yes	characteristic
7	C₈×C₃₄₉	C₈	1	1	yes	characteristic
8	C₈×C₃₄₉	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₃₄₉	C₁₆	1	1	yes	characteristic
10	C₄×C₃₄₉	C₁₆	1	1	yes	characteristic
11	C₄×C₃₄₉	C₂×C₈	1	1	yes	characteristic
12	C₂×C₃₄₉	C₃₂	1	2	yes	complemented
13	C₂×C₃₄₉	C₂×C₁₆	1	1	yes	characteristic
14	C₃₄₉	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	349	1	no	maximal, Sylow
16	C₂×C₁₆	—	349	1	no	—
17	C₃₂	—	349	2	no	—
18	C₂×C₈	#13063703	1	1	yes	characteristic
19	C₁₆	—	349	1	no	—
20	C₁₆	—	349	1	no	—
21	C₂×C₄	#14584102	1	1	yes	characteristic
22	C₈	#14584102	1	1	yes	characteristic
23	C₈	C₂×#13063703	1	1	yes	characteristic
24	C₂²	#19150236	1	1	yes	characteristic
25	C₄	#19150236	1	1	yes	characteristic
26	C₄	C₂×#14584102	1	1	yes	characteristic
27	C₂	#26013689	1	2	yes	direct product factor
28	C₂	C₂×#19150236	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.