Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28357265 | C2 | semidirect |
| 2. #28357246 | C2 | semidirect |
| 3. #28357244 | C2 | semidirect |
| 4. #28357242 | C2 | semidirect |
| 5. #28357239 | C2 | semidirect |
| 6. D8×D433 | C2 | semidirect |
| 7. #28357226 | C2 | semidirect |
| 8. C2×D8×C433 | C2 | semidirect |
| 10. #20294097 | C22 | semidirect |
| 12. #20294096 | C22 | semidirect |
| 15. D4×D433 | C22 | semidirect |
| 16. Dic1732 | C22 | semidirect |
| 17. #20294086 | C22 | semidirect |
| 18. #20294085 | C22 | semidirect |
| 19. D3464 | C22 | semidirect |
| 20. #20294082 | C22 | semidirect |
| 21. #20294081 | C22 | semidirect |
| 22. #20294080 | C22 | semidirect |
| 23. C8×D433 | C22 | semidirect |
| 24. C2×D4×C433 | C22 | semidirect |
| 25. D8×C433 | C22 | semidirect |
| 26. D8×C433 | C22 | semidirect |
| 27. C2×C8×C433 | C22 | semidirect |
| 62. C433 | #576 | semidirect |
| 70. C2×D8 | D433 | semidirect |
| 79. C2×D4 | C2×D433 | semidirect |
| 85. D8 | C2×D433 | semidirect |
| 86. D8 | C2×D433 | semidirect |
| 90. C2×C8 | C2×D433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357265 | 2 |
| #28357246 | 2 |
| #28357244 | 2 |
| #28357242 | 2 |
| #28357239 | 2 |
| D8×D433 | 2 |
| #28357226 | 2 |
| C2×D8×C433 | 2 |
| #576 | 433 |