Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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. C7×#930 | C2 | semidirect |
| 3. C2×C7×D24 | C2 | semidirect |
| 4. C2×C7×#204 | C2 | semidirect |
| 5. C3×C7×C22⋊C8 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#816 | C2 | semidirect |
| 30. C7×C22⋊C8 | D3 | semidirect |
| 31. #4734 | C7 | direct (N × H) |
| 46. C7×D12 | D4 | semidirect |
| 49. C7×Dic6 | D4 | semidirect |
| 67. C2×#235 | C2×C7 | semidirect |
| 68. #930 | C2×C7 | semidirect |
| 69. C2×D24 | C2×C7 | semidirect |
| 70. C2×#204 | C2×C7 | semidirect |
| 71. C3×C22⋊C8 | C2×C7 | semidirect |
| 72. #821 | C2×C7 | semidirect |
| 73. #816 | C2×C7 | semidirect |
| 137. C22⋊C8 | D3×C7 | semidirect |
| 167. D12 | C7×D4 | semidirect |
| 170. Dic6 | C7×D4 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 230. C7 | #4734 | direct (N × H) |
| 252. C3 | C7×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C7×#930 | 2 |
| C2×C7×D24 | 2 |
| C2×C7×#204 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#821 | 2 |
| C7×#816 | 2 |
| C7×#449 | 3 |
| #4734 | 7 |