Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 56 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. C7×#904 | C2 | semidirect |
| 2. C2×C3×D56 | C2 | semidirect |
| 3. #10620651 | C2 | semidirect |
| 4. #10620475 | C2 | semidirect |
| 5. #10620472 | C2 | semidirect |
| 10. C7×Dic12 | C22 | semidirect |
| 11. C7×D24 | C22 | semidirect |
| 15. C3⋊(C7⋊C16) | C22 | semidirect |
| 17. C2×D56 | D3 | semidirect |
| 42. #904 | D7 | semidirect |
| 69. Dic12 | C2×D7 | semidirect |
| 70. D24 | C2×D7 | semidirect |
| 99. C3×C7 | #509 | semidirect |
| 130. C7 | #5147 | semidirect |
| 142. C3 | #89965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#904 | 2 |
| C2×C3×D56 | 2 |
| #10620651 | 2 |
| #10620475 | 2 |
| #10620472 | 2 |
| #89965 | 3 |
| #5147 | 7 |