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. #28352236 | C2 | semidirect |
| 2. #28352235 | C2 | semidirect |
| 3. #28352222 | C2 | semidirect |
| 4. #28352217 | C2 | semidirect |
| 5. #28352211 | C2 | semidirect |
| 6. C2×#20293789 | C2 | semidirect |
| 7. #131×C431 | C2 | semidirect |
| 10. #20293800 | C22 | semidirect |
| 12. C2×Dic862 | C22 | semidirect |
| 16. Dic1724 | C22 | semidirect |
| 17. #20293789 | C22 | semidirect |
| 18. #20293789 | C22 | semidirect |
| 19. #20293789 | C22 | semidirect |
| 20. D3448 | C22 | semidirect |
| 22. M16×C431 | C22 | semidirect |
| 23. C2×C8×C431 | C22 | semidirect |
| 53. C431 | #577 | semidirect |
| 61. #131 | D431 | semidirect |
| 76. M16 | C2×D431 | semidirect |
| 77. C2×C8 | C2×D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352236 | 2 |
| #28352235 | 2 |
| #28352222 | 2 |
| #28352217 | 2 |
| #28352211 | 2 |
| C2×#20293789 | 2 |
| #131×C431 | 2 |
| #577 | 431 |