Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 82 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. C7×#940 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C2×C7×D24 | C2 | semidirect |
| 4. C7×#893 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C7×Dic3⋊C8 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 28. C7×#102 | D3 | semidirect |
| 29. #4786 | C7 | direct (N × H) |
| 44. C7×D12 | D4 | semidirect |
| 61. #940 | C2×C7 | semidirect |
| 62. C2×#213 | C2×C7 | semidirect |
| 63. C2×D24 | C2×C7 | semidirect |
| 64. #893 | C2×C7 | semidirect |
| 65. C3×#102 | C2×C7 | semidirect |
| 66. Dic3⋊C8 | C2×C7 | semidirect |
| 67. #809 | C2×C7 | semidirect |
| 82. C7×Dic3 | D8 | semidirect |
| 127. #102 | D3×C7 | semidirect |
| 157. D12 | C7×D4 | semidirect |
| 161. C3×C7 | #459 | semidirect |
| 195. Dic3 | C7×D8 | semidirect |
| 214. C7 | #4786 | direct (N × H) |
| 236. C3 | C7×#459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#940 | 2 |
| C2×C7×#213 | 2 |
| C2×C7×D24 | 2 |
| C7×#893 | 2 |
| C3×C7×#102 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#809 | 2 |
| C7×#459 | 3 |
| #4786 | 7 |