Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
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. #27159379 | C2 | semidirect |
| 2. #27159375 | C2 | semidirect |
| 3. #27159373 | C2 | semidirect |
| 4. #27159369 | C2 | semidirect |
| 5. #27159360 | C2 | semidirect |
| 7. C4×D1556 | C2 | semidirect |
| 8. C4×D1556 | C2 | semidirect |
| 9. #27159341 | C2 | semidirect |
| 10. C42×D389 | C2 | semidirect |
| 11. C4×Q8×C389 | C2 | semidirect |
| 74. C389 | #529 | semidirect |
| 82. C4×Q8 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159379 | 2 |
| #27159375 | 2 |
| #27159373 | 2 |
| #27159369 | 2 |
| #27159360 | 2 |
| #27159359 | 2 |
| C4×D1556 | 2 |
| #27159341 | 2 |
| C42×D389 | 2 |
| C4×Q8×C389 | 2 |
| #529 | 389 |