Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
462 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 101 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×C4⋊(C3⋊AGL(1,𝔽7)) | C2 | semidirect |
| 2. C2×ΓL(1,𝔽8)×D12 | C2 | semidirect |
| 3. C2×#4247⋊C3 | C2 | semidirect |
| 4. C3×C4×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 5. #10621013 | C3 | semidirect |
| 14. C2×D84 | C2×C3 | semidirect |
| 15. C2×C7×D12 | C2×C3 | semidirect |
| 17. C2×#4247 | C2×C3 | semidirect |
| 20. C3×C4×Dic7 | C2×C3 | semidirect |
| 22. C4×ΓL(1,𝔽8)⋊C4 | D3 | semidirect |
| 29. C3×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 30. C3×ΓL(1,𝔽8)⋊C4 | D4 | semidirect |
| 59. C4×Dic7 | C3×D3 | semidirect |
| 73. C3×C4×C7 | C3×D4 | semidirect |
| 74. C3×Dic7 | C3×D4 | semidirect |
| 76. C4×ΓL(1,𝔽8) | D12 | semidirect |
| 78. ΓL(1,𝔽8)⋊C4 | D12 | semidirect |
| 86. C3×ΓL(1,𝔽8) | #127 | semidirect |
| 99. C2×D12 | AGL(1,𝔽7) | semidirect |
| 126. C4×C7 | C3×D12 | semidirect |
| 127. Dic7 | C3×D12 | semidirect |
| 144. C3×C7 | C3×#127 | semidirect |
| 146. ΓL(1,𝔽8) | #874 | semidirect |
| 175. C3×C4 | (C22⋊D7)⋊C3 | semidirect |
| 184. C7 | C3×#874 | semidirect |
| 201. C4 | #4247⋊C3 | semidirect |
| 204. C3 | #6503⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊AGL(1,𝔽7)) | 2 |
| C2×ΓL(1,𝔽8)×D12 | 2 |
| C2×#4247⋊C3 | 2 |
| C3×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| #10621013 | 3 |
| #6503⋊C3 | 3 |
| C3×#874 | 7 |