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×#239 | C2 | semidirect |
| 2. C2×C3×C7×Q16 | C2 | semidirect |
| 3. C2×C7×#215 | C2 | semidirect |
| 4. C7×#919 | C2 | direct (N × H) |
| 5. C2×C7×D24 | C2 | semidirect |
| 6. C2×D3×C7×C8 | C2 | semidirect |
| 10. C7×#239 | C22 | semidirect |
| 15. C3×C7×Q16 | C22 | semidirect |
| 17. C7×#215 | C22 | semidirect |
| 19. C7×D24 | C22 | semidirect |
| 20. D3×C7×C8 | C22 | semidirect |
| 23. C2×C7×Q16 | D3 | semidirect |
| 27. C2×#919 | C7 | direct (N × H) |
| 50. C7×Q16 | C2×D3 | semidirect |
| 56. C2×#239 | C2×C7 | semidirect |
| 57. C2×C3×Q16 | C2×C7 | semidirect |
| 58. C2×#215 | C2×C7 | semidirect |
| 59. #919 | C2×C7 | direct (N × H) |
| 60. C2×D24 | C2×C7 | semidirect |
| 61. C2×D3×C8 | C2×C7 | semidirect |
| 89. #239 | C22×C7 | semidirect |
| 94. C3×Q16 | C22×C7 | semidirect |
| 96. #215 | C22×C7 | semidirect |
| 98. D24 | C22×C7 | semidirect |
| 99. D3×C8 | C22×C7 | semidirect |
| 100. C2×C3×C7 | #135 | semidirect |
| 106. C2×Q16 | D3×C7 | semidirect |
| 134. C3×C7 | C2×#135 | semidirect |
| 142. Q16 | C2×D3×C7 | semidirect |
| 150. C2×C7 | #919 | direct (N × H) |
| 176. C7 | C2×#919 | direct (N × H) |
| 177. C2×C3 | C7×#135 | semidirect |
| 190. C3 | C2×C7×#135 | semidirect |
| 193. C2 | C7×#919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#239 | 2 |
| C2×C3×C7×Q16 | 2 |
| C2×C7×#215 | 2 |
| C7×#919 | 2 |
| C2×C7×D24 | 2 |
| C2×D3×C7×C8 | 2 |
| C2×C7×#135 | 3 |
| C2×#919 | 7 |