Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 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. #28352184 | C2 | semidirect |
| 2. #28352182 | C2 | semidirect |
| 3. #28352179 | C2 | semidirect |
| 4. #28352175 | C2 | semidirect |
| 5. #28352174 | C2 | semidirect |
| 6. #28352171 | C2 | semidirect |
| 7. #28352167 | C2 | semidirect |
| 9. C4×Dic862 | C2 | semidirect |
| 10. C4×D1724 | C2 | semidirect |
| 11. C4×C22⋊D431 | C2 | semidirect |
| 12. C4×C22⋊D431 | C2 | semidirect |
| 13. #28352146 | C2 | semidirect |
| 14. C42×D431 | C2 | semidirect |
| 15. #117×C431 | C2 | semidirect |
| 103. C431 | #529 | semidirect |
| 118. #117 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352184 | 2 |
| #28352182 | 2 |
| #28352179 | 2 |
| #28352175 | 2 |
| #28352174 | 2 |
| #28352171 | 2 |
| #28352167 | 2 |
| #28352162 | 2 |
| C4×Dic862 | 2 |
| C4×D1724 | 2 |
| C4×C22⋊D431 | 2 |
| #28352146 | 2 |
| C42×D431 | 2 |
| #117×C431 | 2 |
| #529 | 431 |