Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
1532 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 1532 conjugacy classes of subgroups — too many to draw. Only its 267 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. ΓL(1,𝔽8)×#585 | C2 | semidirect |
| 2. #90519⋊C3 | C2 | semidirect |
| 3. #13052144 | C2 | semidirect |
| 4. #13052141 | C2 | semidirect |
| 5. #90012⋊C3 | C2 | semidirect |
| 6. #11741570 | C3 | semidirect |
| 12. C22×C4×AGL(1,𝔽7) | C22 | semidirect |
| 15. #6500⋊C3 | C22 | semidirect |
| 16. #6498⋊C3 | C22 | semidirect |
| 18. #6489⋊C3 | C22 | semidirect |
| 19. #6408⋊C3 | C22 | semidirect |
| 20. C7×#585 | C2×C3 | semidirect |
| 21. #90519 | C2×C3 | semidirect |
| 22. #90016 | C2×C3 | semidirect |
| 23. #90015 | C2×C3 | semidirect |
| 24. #90012 | C2×C3 | semidirect |
| 33. C2×Q8×ΓL(1,𝔽8) | D4 | semidirect |
| 36. C2×D4×ΓL(1,𝔽8) | D4 | semidirect |
| 39. C22×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 56. C22×C4×D7 | C22×C3 | semidirect |
| 59. #6500 | C22×C3 | semidirect |
| 60. #6498 | C22×C3 | semidirect |
| 62. #6489 | C22×C3 | semidirect |
| 63. #6408 | C22×C3 | semidirect |
| 98. C2×C7×Q8 | C3×D4 | semidirect |
| 101. C2×C7×D4 | C3×D4 | semidirect |
| 104. C22×C4×C7 | C3×D4 | semidirect |
| 142. #585 | AGL(1,𝔽7) | semidirect |
| 244. ΓL(1,𝔽8) | #3025 | semidirect |
| 252. C2×Q8 | (C22⋊D7)⋊C3 | semidirect |
| 256. C2×D4 | (C22⋊D7)⋊C3 | semidirect |
| 262. C22×C4 | (C22⋊D7)⋊C3 | semidirect |
| 308. C7 | C3×#3025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#585 | 2 |
| #90519⋊C3 | 2 |
| #13052144 | 2 |
| #13052141 | 2 |
| #90012⋊C3 | 2 |
| #11741570 | 3 |
| C3×#3025 | 7 |