Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 62 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. #10621430 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. #10620997 | C2 | semidirect |
| 5. C3×#6409 | C2 | semidirect |
| 6. #10620518 | C2 | semidirect |
| 7. #10620503 | C2 | semidirect |
| 26. #6409 | D3 | semidirect |
| 60. C2×#215 | D7 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | #4819 | semidirect |
| 217. C3 | #89937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621430 | 2 |
| C2×C7×#215 | 2 |
| #10620997 | 2 |
| C2×#66562 | 2 |
| C3×#6409 | 2 |
| #10620518 | 2 |
| #10620503 | 2 |
| #89937 | 3 |
| #4819 | 7 |