Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27159382 | C2 | semidirect |
| 2. #27159379 | C2 | semidirect |
| 3. #27159377 | C2 | semidirect |
| 4. #27159373 | C2 | semidirect |
| 5. #27159370 | C2 | semidirect |
| 6. #27159370 | C2 | semidirect |
| 7. #27159369 | C2 | semidirect |
| 8. #27159367 | C2 | semidirect |
| 9. #27159362 | C2 | semidirect |
| 10. #27159362 | C2 | semidirect |
| 12. #27159349 | C2 | semidirect |
| 13. C4×C22⋊D389 | C2 | semidirect |
| 14. #27159342 | C2 | semidirect |
| 15. C22⋊Q8×C389 | C2 | semidirect |
| 103. C389 | #542 | semidirect |
| 115. C22⋊Q8 | D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159382 | 2 |
| #27159379 | 2 |
| #27159377 | 2 |
| #27159373 | 2 |
| #27159370 | 2 |
| #27159369 | 2 |
| #27159367 | 2 |
| #27159362 | 2 |
| #27159357 | 2 |
| #27159349 | 2 |
| C4×C22⋊D389 | 2 |
| #27159342 | 2 |
| C22⋊Q8×C389 | 2 |
| #542 | 389 |