Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 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. #27159429 | C2 | semidirect |
| 2. #27159410 | C2 | semidirect |
| 3. #27159408 | C2 | semidirect |
| 4. #27159406 | C2 | semidirect |
| 5. #27159403 | C2 | semidirect |
| 6. D8×D389 | C2 | semidirect |
| 7. #27159390 | C2 | semidirect |
| 8. C2×D8×C389 | C2 | semidirect |
| 10. #20261966 | C22 | semidirect |
| 12. #20261965 | C22 | semidirect |
| 15. D4×D389 | C22 | semidirect |
| 16. Dic1556 | C22 | semidirect |
| 17. #20261955 | C22 | semidirect |
| 18. #20261954 | C22 | semidirect |
| 19. D3112 | C22 | semidirect |
| 20. #20261951 | C22 | semidirect |
| 21. #20261950 | C22 | semidirect |
| 22. #20261949 | C22 | semidirect |
| 23. C8×D389 | C22 | semidirect |
| 24. C2×D4×C389 | C22 | semidirect |
| 25. D8×C389 | C22 | semidirect |
| 26. D8×C389 | C22 | semidirect |
| 27. C2×C8×C389 | C22 | semidirect |
| 62. C389 | #576 | semidirect |
| 70. C2×D8 | D389 | semidirect |
| 79. C2×D4 | C2×D389 | semidirect |
| 85. D8 | C2×D389 | semidirect |
| 86. D8 | C2×D389 | semidirect |
| 90. C2×C8 | C2×D389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27159429 | 2 |
| #27159410 | 2 |
| #27159408 | 2 |
| #27159406 | 2 |
| #27159403 | 2 |
| D8×D389 | 2 |
| #27159390 | 2 |
| C2×D8×C389 | 2 |
| #576 | 389 |