Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #28352235 | C2 | semidirect |
| 2. #28352220 | C2 | semidirect |
| 3. #28352214 | C2 | semidirect |
| 4. #28352209 | C2 | semidirect |
| 5. C2×#20293787 | C2 | semidirect |
| 6. #28352196 | C2 | semidirect |
| 7. 2−1+4×C431 | C2 | semidirect |
| 12. #20293790 | C22 | semidirect |
| 13. #20293788 | C22 | semidirect |
| 14. #20293787 | C22 | semidirect |
| 15. #20293787 | C22 | semidirect |
| 16. #20293785 | C22 | semidirect |
| 17. #20293784 | C22 | semidirect |
| 18. C2×C431⋊C8 | C22 | semidirect |
| 21. #41×C431 | C22 | semidirect |
| 23. C2×Q8×C431 | C22 | semidirect |
| 53. C431 | #577 | semidirect |
| 55. 2−1+4 | D431 | semidirect |
| 66. #41 | C2×D431 | semidirect |
| 68. C2×Q8 | C2×D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352235 | 2 |
| #28352220 | 2 |
| #28352214 | 2 |
| #28352209 | 2 |
| C2×#20293787 | 2 |
| #28352196 | 2 |
| 2−1+4×C431 | 2 |
| #577 | 431 |