Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
536 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 186 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. #10621518 | C2 | semidirect |
| 2. ΓL(1,𝔽8)×#131 | C2 | semidirect |
| 3. #6471⋊C3 | C2 | semidirect |
| 4. #6467⋊C3 | C2 | semidirect |
| 5. C2×D56⋊C3 | C2 | semidirect |
| 6. #90443 | C3 | semidirect |
| 10. #1157⋊C3 | C22 | semidirect |
| 11. C2×C4⋊AGL(1,𝔽7) | C22 | semidirect |
| 12. M16×ΓL(1,𝔽8) | C22 | semidirect |
| 13. C2×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 14. Dic28⋊C3 | C22 | semidirect |
| 15. D56⋊C3 | C22 | semidirect |
| 16. D56⋊C3 | C22 | semidirect |
| 17. #1132⋊C3 | C22 | semidirect |
| 18. #6553 | C2×C3 | semidirect |
| 19. C7×#131 | C2×C3 | semidirect |
| 20. #6471 | C2×C3 | semidirect |
| 21. #6467 | C2×C3 | semidirect |
| 22. C2×D56 | C2×C3 | semidirect |
| 38. #1157 | C22×C3 | semidirect |
| 39. C2×D28 | C22×C3 | semidirect |
| 40. C7×M16 | C22×C3 | semidirect |
| 41. C2×C7×C8 | C22×C3 | semidirect |
| 42. Dic28 | C22×C3 | semidirect |
| 43. D56 | C22×C3 | semidirect |
| 44. D56 | C22×C3 | semidirect |
| 45. #1132 | C22×C3 | semidirect |
| 87. #131 | AGL(1,𝔽7) | semidirect |
| 105. ΓL(1,𝔽8) | #576 | semidirect |
| 115. M16 | C2×AGL(1,𝔽7) | semidirect |
| 116. C2×C8 | C2×AGL(1,𝔽7) | semidirect |
| 137. C7 | C3×#576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621518 | 2 |
| ΓL(1,𝔽8)×#131 | 2 |
| #6471⋊C3 | 2 |
| #6467⋊C3 | 2 |
| C2×D56⋊C3 | 2 |
| #90443 | 3 |
| C3×#576 | 7 |