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. #28357266 | C2 | semidirect |
| 2. #28357247 | C2 | semidirect |
| 3. #28357245 | C2 | semidirect |
| 4. #28357243 | C2 | semidirect |
| 5. C2×D3464 | C2 | semidirect |
| 6. D8×D433 | C2 | semidirect |
| 7. #28357226 | C2 | semidirect |
| 8. #135×C433 | C2 | semidirect |
| 9. #20294098 | C22 | semidirect |
| 13. C2×D1732 | C22 | semidirect |
| 15. D4×D433 | C22 | semidirect |
| 16. #20294084 | C22 | semidirect |
| 17. D3464 | C22 | semidirect |
| 18. D3464 | C22 | semidirect |
| 19. #20294082 | C22 | semidirect |
| 20. #20294081 | C22 | semidirect |
| 21. #20294080 | C22 | semidirect |
| 22. C8×D433 | C22 | semidirect |
| 23. #41×C433 | C22 | semidirect |
| 24. Q16×C433 | C22 | semidirect |
| 25. SD16×C433 | C22 | semidirect |
| 26. D8×C433 | C22 | semidirect |
| 27. C2×C8×C433 | C22 | semidirect |
| 62. C433 | #576 | semidirect |
| 68. #135 | D433 | semidirect |
| 75. #41 | C2×D433 | semidirect |
| 80. Q16 | C2×D433 | semidirect |
| 82. SD16 | 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 |
|---|---|
| #28357266 | 2 |
| #28357247 | 2 |
| #28357245 | 2 |
| #28357243 | 2 |
| C2×D3464 | 2 |
| D8×D433 | 2 |
| #28357226 | 2 |
| #135×C433 | 2 |
| #576 | 433 |