Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
486 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D4×ΓL(1,𝔽8) | C2 | semidirect |
| 2. C2×ΓL(1,𝔽8)×#67 | C2 | semidirect |
| 3. C2×ΓL(1,𝔽8)×D12 | C2 | semidirect |
| 4. C4×Dic3×ΓL(1,𝔽8) | C2 | semidirect |
| 5. C7×#940 | C3 | semidirect |
| 14. C2×C3×C7×D4 | C2×C3 | semidirect |
| 15. C2×C7×#67 | C2×C3 | semidirect |
| 16. C2×C7×D12 | C2×C3 | semidirect |
| 20. C2×D4×ΓL(1,𝔽8) | D3 | semidirect |
| 21. C4×C7×Dic3 | C2×C3 | semidirect |
| 29. C3×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 30. Dic3×ΓL(1,𝔽8) | D4 | semidirect |
| 60. C2×C7×D4 | C3×D3 | semidirect |
| 63. #940 | ΓL(1,𝔽8) | direct (N × H) |
| 78. C3×C4×C7 | C3×D4 | semidirect |
| 79. C7×Dic3 | C3×D4 | semidirect |
| 82. C4×ΓL(1,𝔽8) | #67 | semidirect |
| 90. C3×ΓL(1,𝔽8) | #127 | semidirect |
| 102. C2×C3×D4 | C2×ΓL(1,𝔽8) | semidirect |
| 103. C2×#67 | C2×ΓL(1,𝔽8) | semidirect |
| 104. C2×D12 | C2×ΓL(1,𝔽8) | semidirect |
| 106. C4×Dic3 | C2×ΓL(1,𝔽8) | semidirect |
| 133. C4×C7 | C3×#67 | semidirect |
| 152. C3×C7 | C3×#127 | semidirect |
| 154. ΓL(1,𝔽8) | #940 | direct (N × H) |
| 161. C2×D4 | D3×ΓL(1,𝔽8) | semidirect |
| 184. C3×C4 | D4×ΓL(1,𝔽8) | semidirect |
| 185. Dic3 | D4×ΓL(1,𝔽8) | semidirect |
| 194. C7 | C3×#940 | semidirect |
| 213. C4 | ΓL(1,𝔽8)×#67 | semidirect |
| 216. C3 | ΓL(1,𝔽8)×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×ΓL(1,𝔽8) | 2 |
| C2×ΓL(1,𝔽8)×#67 | 2 |
| C2×ΓL(1,𝔽8)×D12 | 2 |
| C4×Dic3×ΓL(1,𝔽8) | 2 |
| C7×#940 | 3 |
| ΓL(1,𝔽8)×#127 | 3 |
| C3×#940 | 7 |