Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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. #10621376 | C2 | semidirect |
| 2. C7×#897 | C2 | semidirect |
| 3. C3×#6453 | C2 | semidirect |
| 5. #10620989 | C2 | semidirect |
| 6. #10620968 | C2 | semidirect |
| 7. C4×D3×Dic7 | C2 | semidirect |
| 8. #10620937 | C2 | semidirect |
| 9. #10620909 | C2 | semidirect |
| 10. #10620906 | C2 | semidirect |
| 11. #10620899 | C2 | semidirect |
| 44. #6453 | D3 | semidirect |
| 91. #897 | D7 | semidirect |
| 208. C3×C7 | #529 | semidirect |
| 271. C7 | #5691 | semidirect |
| 293. C3 | #90315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621376 | 2 |
| C7×#897 | 2 |
| C3×#6453 | 2 |
| #10621022 | 2 |
| #10620989 | 2 |
| #10620968 | 2 |
| C4×D3×Dic7 | 2 |
| #10620937 | 2 |
| #10620909 | 2 |
| #10620906 | 2 |
| #10620899 | 2 |
| #90315 | 3 |
| #5691 | 7 |