Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #28352237 | C2 | semidirect |
| 2. #28352236 | C2 | semidirect |
| 3. #28352222 | C2 | semidirect |
| 4. #28352221 | C2 | semidirect |
| 5. #28352218 | C2 | semidirect |
| 6. #28352210 | C2 | semidirect |
| 7. #28352209 | C2 | semidirect |
| 8. C2×#20293790 | C2 | semidirect |
| 9. Q16×D431 | C2 | semidirect |
| 10. #28352197 | C2 | semidirect |
| 11. #137×C431 | C2 | semidirect |
| 87. C431 | #578 | semidirect |
| 94. #137 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352237 | 2 |
| #28352236 | 2 |
| #28352222 | 2 |
| #28352221 | 2 |
| #28352218 | 2 |
| #28352210 | 2 |
| #28352209 | 2 |
| C2×#20293790 | 2 |
| Q16×D431 | 2 |
| #28352197 | 2 |
| #137×C431 | 2 |
| #578 | 431 |