Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #28352180 | C2 | semidirect |
| 3. #28352178 | C2 | semidirect |
| 4. #28352174 | C2 | semidirect |
| 5. #28352165 | C2 | semidirect |
| 7. C4×D1724 | C2 | semidirect |
| 8. C4×D1724 | C2 | semidirect |
| 9. #28352146 | C2 | semidirect |
| 10. C42×D431 | C2 | semidirect |
| 11. C4×Q8×C431 | C2 | semidirect |
| 74. C431 | #529 | semidirect |
| 82. C4×Q8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352184 | 2 |
| #28352180 | 2 |
| #28352178 | 2 |
| #28352174 | 2 |
| #28352165 | 2 |
| #28352164 | 2 |
| C4×D1724 | 2 |
| #28352146 | 2 |
| C42×D431 | 2 |
| C4×Q8×C431 | 2 |
| #529 | 431 |