Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #27159430 | C2 | semidirect |
| 2. #27159415 | C2 | semidirect |
| 3. #27159409 | C2 | semidirect |
| 4. #27159404 | C2 | semidirect |
| 5. C2×#20261953 | C2 | semidirect |
| 6. #27159391 | C2 | semidirect |
| 7. 2−1+4×C389 | C2 | semidirect |
| 12. #20261956 | C22 | semidirect |
| 13. #20261954 | C22 | semidirect |
| 14. #20261953 | C22 | semidirect |
| 15. #20261953 | C22 | semidirect |
| 16. #20261951 | C22 | semidirect |
| 17. #20261950 | C22 | semidirect |
| 18. C2×#15691005 | C22 | semidirect |
| 21. #41×C389 | C22 | semidirect |
| 23. C2×Q8×C389 | C22 | semidirect |
| 53. C389 | #577 | semidirect |
| 55. 2−1+4 | D389 | semidirect |
| 66. #41 | C2×D389 | semidirect |
| 68. C2×Q8 | C2×D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159430 | 2 |
| #27159415 | 2 |
| #27159409 | 2 |
| #27159404 | 2 |
| C2×#20261953 | 2 |
| #27159391 | 2 |
| 2−1+4×C389 | 2 |
| #577 | 389 |