Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
496 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 126 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. #10621576 | C2 | semidirect |
| 2. #10621402 | C2 | semidirect |
| 3. D3×C7×Q16 | C2 | semidirect |
| 4. C3×D7×Q16 | C2 | semidirect |
| 5. #10621082 | C2 | semidirect |
| 6. #10621077 | C2 | semidirect |
| 7. #10621074 | C2 | semidirect |
| 8. #10620837 | C2 | semidirect |
| 9. #10620833 | C2 | semidirect |
| 10. #10620827 | C2 | semidirect |
| 11. #10620826 | C2 | semidirect |
| 48. D7×Q16 | D3 | semidirect |
| 114. D3×Q16 | D7 | semidirect |
| 237. C3×C7 | #578 | semidirect |
| 308. C7 | #5766 | semidirect |
| 325. C3 | #90457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621576 | 2 |
| #10621402 | 2 |
| D3×C7×Q16 | 2 |
| C3×D7×Q16 | 2 |
| #10621082 | 2 |
| #10621077 | 2 |
| #10621074 | 2 |
| #10620837 | 2 |
| #10620833 | 2 |
| #10620827 | 2 |
| #10620826 | 2 |
| #90457 | 3 |
| #5766 | 7 |