Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 206 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×#237 | C2 | semidirect |
| 2. C2×C3×C7×D8 | C2 | semidirect |
| 3. C2×C7×#214 | C2 | semidirect |
| 4. C7×#912 | C2 | direct (N × H) |
| 5. C2×C7×Dic12 | C2 | semidirect |
| 6. C2×D3×C7×C8 | C2 | semidirect |
| 12. C7×#237 | C22 | semidirect |
| 15. C3×C7×D8 | C22 | semidirect |
| 17. C7×#214 | C22 | semidirect |
| 19. C7×Dic12 | C22 | semidirect |
| 20. D3×C7×C8 | C22 | semidirect |
| 25. C2×C7×D8 | D3 | semidirect |
| 27. C2×#912 | C7 | direct (N × H) |
| 52. C7×D8 | C2×D3 | semidirect |
| 56. C2×#237 | C2×C7 | semidirect |
| 57. C2×C3×D8 | C2×C7 | semidirect |
| 58. C2×#214 | C2×C7 | semidirect |
| 59. #912 | C2×C7 | direct (N × H) |
| 60. C2×Dic12 | C2×C7 | semidirect |
| 61. C2×D3×C8 | C2×C7 | semidirect |
| 91. #237 | C22×C7 | semidirect |
| 94. C3×D8 | C22×C7 | semidirect |
| 96. #214 | C22×C7 | semidirect |
| 98. Dic12 | C22×C7 | semidirect |
| 99. D3×C8 | C22×C7 | semidirect |
| 101. C2×C3×C7 | #135 | semidirect |
| 108. C2×D8 | D3×C7 | semidirect |
| 134. C3×C7 | C2×#135 | semidirect |
| 144. D8 | C2×D3×C7 | semidirect |
| 150. C2×C7 | #912 | direct (N × H) |
| 176. C7 | C2×#912 | direct (N × H) |
| 178. C2×C3 | C7×#135 | semidirect |
| 190. C3 | C2×C7×#135 | semidirect |
| 193. C2 | C7×#912 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| C2×C3×C7×D8 | 2 |
| C2×C7×#214 | 2 |
| C7×#912 | 2 |
| C2×C7×Dic12 | 2 |
| C2×D3×C7×C8 | 2 |
| C2×C7×#135 | 3 |
| C2×#912 | 7 |