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. C3×C7×#121 | C2 | semidirect |
| 3. C2×C7×#214 | C2 | semidirect |
| 4. C2×C7×#213 | C2 | semidirect |
| 5. C7×#830 | C2 | semidirect |
| 6. C7×#810 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 27. C7×#121 | D3 | semidirect |
| 31. #5037 | C7 | direct (N × H) |
| 46. C7×D12 | D4 | semidirect |
| 49. C7×Dic6 | D4 | semidirect |
| 67. C2×#235 | C2×C7 | semidirect |
| 68. C3×#121 | C2×C7 | semidirect |
| 69. C2×#214 | C2×C7 | semidirect |
| 70. C2×#213 | C2×C7 | semidirect |
| 71. #830 | C2×C7 | semidirect |
| 72. #810 | C2×C7 | semidirect |
| 73. #809 | C2×C7 | semidirect |
| 134. #121 | D3×C7 | semidirect |
| 167. D12 | C7×D4 | semidirect |
| 170. Dic6 | C7×D4 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 230. C7 | #5037 | 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 |
| C3×C7×#121 | 2 |
| C2×C7×#214 | 2 |
| C2×C7×#213 | 2 |
| C7×#830 | 2 |
| C7×#810 | 2 |
| C7×#809 | 2 |
| C7×#449 | 3 |
| #5037 | 7 |