Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#20294097 | C2 | semidirect |
| 2. #28357253 | C2 | semidirect |
| 3. #28357248 | C2 | semidirect |
| 4. #28357242 | C2 | semidirect |
| 5. C2×M16×C433 | C2 | semidirect |
| 9. #20294097 | C22 | semidirect |
| 10. C2×Dic866 | C22 | semidirect |
| 11. C2×D1732 | C22 | semidirect |
| 14. Dic1732 | C22 | semidirect |
| 15. #20294086 | C22 | semidirect |
| 16. D3464 | C22 | semidirect |
| 18. M16×C433 | C22 | semidirect |
| 19. C2×C8×C433 | C22 | semidirect |
| 49. C433 | #575 | semidirect |
| 55. C2×M16 | D433 | semidirect |
| 68. M16 | C2×D433 | semidirect |
| 69. C2×C8 | C2×D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294097 | 2 |
| #28357253 | 2 |
| #28357248 | 2 |
| #28357242 | 2 |
| C2×M16×C433 | 2 |
| #575 | 433 |