Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 2. C2×C3×C7×M16 | C2 | semidirect |
| 3. C7×#926 | C2 | semidirect |
| 4. C7×#825 | C2 | semidirect |
| 10. C7×#235 | C4 | semidirect |
| 12. C2×C7×D12 | C4 | semidirect |
| 14. C2×C7×Dic6 | C4 | semidirect |
| 16. C3×C7×M16 | C22 | semidirect |
| 20. C4×C7×Dic3 | C22 | semidirect |
| 22. C2×C7×M16 | D3 | semidirect |
| 25. #5139 | C7 | direct (N × H) |
| 55. C7×M16 | C2×D3 | semidirect |
| 61. C2×C3×M16 | C2×C7 | semidirect |
| 62. #926 | C2×C7 | semidirect |
| 63. #825 | C2×C7 | semidirect |
| 100. #235 | C4×C7 | semidirect |
| 102. C2×D12 | C4×C7 | semidirect |
| 104. C2×Dic6 | C4×C7 | semidirect |
| 106. C3×M16 | C22×C7 | semidirect |
| 110. C4×Dic3 | C22×C7 | semidirect |
| 117. C2×M16 | D3×C7 | semidirect |
| 151. C3×C7 | #421 | semidirect |
| 162. M16 | C2×D3×C7 | semidirect |
| 203. C7 | #5139 | direct (N × H) |
| 221. C3 | C7×#421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×C3×C7×M16 | 2 |
| C7×#926 | 2 |
| C7×#825 | 2 |
| C7×#421 | 3 |
| #5139 | 7 |