Subgroups — C₂×#20295865 #28378199

Order 13952.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295865	C₂	1	2	yes	maximal, direct product factor
2	C₂×#16812605	C₂	1	1	yes	maximal, characteristic
3	#16812605	C₄	1	1	yes	characteristic
4	#16812605	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₁₀₉	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₀₉	C₈	1	1	yes	characteristic
7	C₁₆×C₁₀₉	C₈	1	1	yes	characteristic
8	C₁₆×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	C₁₆	1	1	yes	characteristic
10	C₈×C₁₀₉	C₁₆	1	1	yes	characteristic
11	C₈×C₁₀₉	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₀₉	C₃₂	1	1	yes	characteristic
13	C₄×C₁₀₉	C₃₂	1	1	yes	characteristic
14	C₄×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₀₉	C₆₄	1	2	yes	complemented
16	C₂×C₁₀₉	C₂×C₃₂	1	1	yes	characteristic
17	C₂×C₆₄	—	109	1	no	maximal, Sylow
18	C₁₀₉	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	—	109	1	no	—
20	C₆₄	—	109	2	no	—
21	C₂×C₁₆	#89137	1	1	yes	characteristic
22	C₃₂	—	109	1	no	—
23	C₃₂	—	109	1	no	—
24	C₂×C₈	#11724786	1	1	yes	characteristic
25	C₁₆	#11724786	1	1	yes	characteristic
26	C₁₆	C₂×#89137	1	1	yes	characteristic
27	C₂×C₄	#13182032	1	1	yes	characteristic
28	C₈	#13182032	1	1	yes	characteristic
29	C₈	C₂×#11724786	1	1	yes	characteristic
30	C₂²	#16812749	1	1	yes	characteristic
31	C₄	#16812749	1	1	yes	characteristic
32	C₄	C₂×#13182032	1	1	yes	characteristic
33	C₂	#20295865	1	2	yes	direct product factor
34	C₂	C₂×#16812749	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.