Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 4. #10620649 | C2 | semidirect |
| 5. C7×#810 | C2 | semidirect |
| 6. #10620509 | C2 | semidirect |
| 7. #10620507 | C2 | semidirect |
| 15. D7×Dic6 | C4 | semidirect |
| 68. #810 | D7 | semidirect |
| 151. C3×C7 | #419 | semidirect |
| 198. C7 | #5004 | semidirect |
| 214. C3 | #89574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×Dic6 | 2 |
| C3×#6455 | 2 |
| C2×#66557 | 2 |
| #10620649 | 2 |
| C7×#810 | 2 |
| #10620509 | 2 |
| #10620507 | 2 |
| #89574 | 3 |
| #5004 | 7 |