Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
524 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 214 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×C7×#235 | C2 | semidirect |
| 2. C2×C3×C7×M16 | C2 | semidirect |
| 3. C7×#909 | C2 | semidirect |
| 4. C7×#908 | C2 | semidirect |
| 5. C7×#904 | C2 | semidirect |
| 12. C7×#235 | C22 | semidirect |
| 13. C2×C7×D12 | C22 | semidirect |
| 15. C2×C7×Dic6 | C22 | semidirect |
| 16. C3×C7×M16 | C22 | semidirect |
| 17. C2×C3×C7×C8 | C22 | semidirect |
| 18. C7×Dic12 | C22 | semidirect |
| 19. C7×D24 | C22 | semidirect |
| 20. C7×#204 | C22 | semidirect |
| 25. C2×C7×M16 | D3 | semidirect |
| 26. #5748 | C7 | direct (N × H) |
| 55. C7×M16 | C2×D3 | semidirect |
| 56. C2×C7×C8 | C2×D3 | semidirect |
| 57. C2×#235 | C2×C7 | semidirect |
| 58. C2×C3×M16 | C2×C7 | semidirect |
| 59. #909 | C2×C7 | semidirect |
| 60. #908 | C2×C7 | semidirect |
| 61. #904 | C2×C7 | semidirect |
| 93. #235 | C22×C7 | semidirect |
| 94. C2×D12 | C22×C7 | semidirect |
| 96. C2×Dic6 | C22×C7 | semidirect |
| 97. C3×M16 | C22×C7 | semidirect |
| 98. C2×C3×C8 | C22×C7 | semidirect |
| 99. Dic12 | C22×C7 | semidirect |
| 100. D24 | C22×C7 | semidirect |
| 101. #204 | C22×C7 | semidirect |
| 110. C2×M16 | D3×C7 | semidirect |
| 136. C3×C7 | #575 | semidirect |
| 149. M16 | C2×D3×C7 | semidirect |
| 150. C2×C8 | C2×D3×C7 | semidirect |
| 180. C7 | #5748 | direct (N × H) |
| 194. C3 | C7×#575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×C3×C7×M16 | 2 |
| C7×#909 | 2 |
| C7×#908 | 2 |
| C7×#904 | 2 |
| C7×#575 | 3 |
| #5748 | 7 |