Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
524 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 524 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. C2×#1157⋊C3 | C2 | semidirect |
| 2. C2×M16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #6472⋊C3 | C2 | semidirect |
| 4. #6471⋊C3 | C2 | semidirect |
| 5. #6467⋊C3 | C2 | semidirect |
| 6. #90439 | C3 | semidirect |
| 12. #1157⋊C3 | C22 | semidirect |
| 13. C2×C4⋊AGL(1,𝔽7) | C22 | semidirect |
| 15. C2×ΓL(1,𝔽8)⋊Q8 | C22 | semidirect |
| 16. M16×ΓL(1,𝔽8) | C22 | semidirect |
| 17. C2×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 18. Dic28⋊C3 | C22 | semidirect |
| 19. D56⋊C3 | C22 | semidirect |
| 20. #1132⋊C3 | C22 | semidirect |
| 21. C2×#1157 | C2×C3 | semidirect |
| 22. C2×C7×M16 | C2×C3 | semidirect |
| 23. #6472 | C2×C3 | semidirect |
| 24. #6471 | C2×C3 | semidirect |
| 25. #6467 | C2×C3 | semidirect |
| 48. #1157 | C22×C3 | semidirect |
| 49. C2×D28 | C22×C3 | semidirect |
| 51. C2×Dic14 | C22×C3 | semidirect |
| 52. C7×M16 | C22×C3 | semidirect |
| 53. C2×C7×C8 | C22×C3 | semidirect |
| 54. Dic28 | C22×C3 | semidirect |
| 55. D56 | C22×C3 | semidirect |
| 56. #1132 | C22×C3 | semidirect |
| 110. C2×M16 | AGL(1,𝔽7) | semidirect |
| 136. ΓL(1,𝔽8) | #575 | semidirect |
| 149. M16 | C2×AGL(1,𝔽7) | semidirect |
| 150. C2×C8 | C2×AGL(1,𝔽7) | semidirect |
| 180. C7 | C3×#575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C2×M16×ΓL(1,𝔽8) | 2 |
| #6472⋊C3 | 2 |
| #6471⋊C3 | 2 |
| #6467⋊C3 | 2 |
| #90439 | 3 |
| C3×#575 | 7 |