Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 64 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×#215 | C2 | semidirect |
| 2. C3×#6510 | C2 | semidirect |
| 3. D12×Dic7 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 7. #10620500 | C2 | semidirect |
| 23. #6510 | D3 | semidirect |
| 60. C2×#215 | D7 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | #5057 | semidirect |
| 217. C3 | #89937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#215 | 2 |
| C3×#6510 | 2 |
| D12×Dic7 | 2 |
| C2×#66560 | 2 |
| #10620674 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620500 | 2 |
| #89937 | 3 |
| #5057 | 7 |