Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 90 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×D3×C7×Q8 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C2×C7×#204 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 6. C7×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 29. C7×#103 | D3 | semidirect |
| 31. #4806 | C7 | direct (N × H) |
| 35. C3×C7×Q8 | D4 | semidirect |
| 49. C7×Dic6 | D4 | semidirect |
| 67. C2×D3×Q8 | C2×C7 | semidirect |
| 68. C2×#215 | C2×C7 | semidirect |
| 69. C2×#204 | C2×C7 | semidirect |
| 71. C3×#103 | C2×C7 | semidirect |
| 72. (C2×D3)⋊C8 | C2×C7 | semidirect |
| 73. #810 | C2×C7 | semidirect |
| 80. C2×D3×C7 | SD16 | semidirect |
| 94. C7×Q8 | D12 | semidirect |
| 133. #103 | D3×C7 | semidirect |
| 151. C3×Q8 | C7×D4 | semidirect |
| 165. Dic6 | C7×D4 | semidirect |
| 168. C3×C7 | #448 | semidirect |
| 195. C2×D3 | C7×SD16 | semidirect |
| 208. Q8 | C7×D12 | semidirect |
| 222. C7 | #4806 | direct (N × H) |
| 241. C3 | C7×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| C2×C7×#215 | 2 |
| C2×C7×#204 | 2 |
| C7×#895 | 2 |
| C3×C7×#103 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#810 | 2 |
| C7×#448 | 3 |
| #4806 | 7 |