Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #20299080 | C2 | semidirect |
| 3. #20298711 | C2 | semidirect |
| 4. #20298709 | C2 | semidirect |
| 5. #20298705 | C2 | semidirect |
| 6. C4×#14268634 | C2 | semidirect |
| 7. #20298683 | C2 | semidirect |
| 8. #106×D113 | C2 | semidirect |
| 9. #20298598 | C2 | semidirect |
| 10. #20298555 | C2 | semidirect |
| 11. #441×C113 | C2 | semidirect |
| 13. #16813645 | C4 | semidirect |
| 41. #14268648 | C2×C4 | semidirect |
| 49. #14268634 | C2×C4 | semidirect |
| 50. D904 | C2×C4 | semidirect |
| 54. C8×D113 | C2×C4 | semidirect |
| 65. Q16×C113 | C2×C4 | semidirect |
| 115. C113 | #2952 | semidirect |
| 121. #441 | D113 | semidirect |
| 165. Q16 | C4×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813645 | 2 |
| #20299080 | 2 |
| #20298711 | 2 |
| #20298709 | 2 |
| #20298705 | 2 |
| C4×#14268634 | 2 |
| #20298683 | 2 |
| #106×D113 | 2 |
| #20298598 | 2 |
| #20298555 | 2 |
| #441×C113 | 2 |
| #2952 | 113 |