Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 102 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×D4×Dic3 | C2 | semidirect |
| 3. C7×#893 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. C7×#821 | C2 | semidirect |
| 6. C7×C8×Dic3 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 16. C7×#213 | C4 | semidirect |
| 26. C7×#102 | D3 | semidirect |
| 28. #4756 | C7 | direct (N × H) |
| 32. C3×C7×D4 | C2×C4 | semidirect |
| 40. C7×D12 | C2×C4 | semidirect |
| 43. C7×C3⋊C8 | C2×C4 | semidirect |
| 56. D4×Dic3 | C2×C7 | semidirect |
| 58. #893 | C2×C7 | semidirect |
| 59. C3×#102 | C2×C7 | semidirect |
| 60. #821 | C2×C7 | semidirect |
| 61. C8×Dic3 | C2×C7 | semidirect |
| 62. #807 | C2×C7 | semidirect |
| 75. C7×Dic3 | D8 | semidirect |
| 82. C7×D4 | C4×D3 | semidirect |
| 99. #213 | C4×C7 | semidirect |
| 114. #102 | D3×C7 | semidirect |
| 132. C3×D4 | C2×C4×C7 | semidirect |
| 140. D12 | C2×C4×C7 | semidirect |
| 143. C3⋊C8 | C2×C4×C7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 174. Dic3 | C7×D8 | semidirect |
| 180. D4 | C4×D3×C7 | semidirect |
| 190. C7 | #4756 | direct (N × H) |
| 209. C3 | C4×C7×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Dic3 | 2 |
| C2×C7×#213 | 2 |
| C7×#893 | 2 |
| C3×C7×#102 | 2 |
| C7×#821 | 2 |
| C7×C8×Dic3 | 2 |
| C7×#807 | 2 |
| C4×C7×D8 | 3 |
| #4756 | 7 |