Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
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. #27163141 | C2 | semidirect |
| 2. #27163122 | C2 | semidirect |
| 3. #27163120 | C2 | semidirect |
| 4. #27163118 | C2 | semidirect |
| 5. #27163115 | C2 | semidirect |
| 6. D8×D397 | C2 | semidirect |
| 7. #27163102 | C2 | semidirect |
| 8. C2×D8×C397 | C2 | semidirect |
| 10. #20263731 | C22 | semidirect |
| 12. #20263730 | C22 | semidirect |
| 15. D4×D397 | C22 | semidirect |
| 16. Dic1588 | C22 | semidirect |
| 17. #20263720 | C22 | semidirect |
| 18. #20263719 | C22 | semidirect |
| 19. D3176 | C22 | semidirect |
| 20. #20263716 | C22 | semidirect |
| 21. #20263715 | C22 | semidirect |
| 22. #20263714 | C22 | semidirect |
| 23. C8×D397 | C22 | semidirect |
| 24. C2×D4×C397 | C22 | semidirect |
| 25. D8×C397 | C22 | semidirect |
| 26. D8×C397 | C22 | semidirect |
| 27. C2×C8×C397 | C22 | semidirect |
| 62. C397 | #576 | semidirect |
| 70. C2×D8 | D397 | semidirect |
| 79. C2×D4 | C2×D397 | semidirect |
| 85. D8 | C2×D397 | semidirect |
| 86. D8 | C2×D397 | semidirect |
| 90. C2×C8 | C2×D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163141 | 2 |
| #27163122 | 2 |
| #27163120 | 2 |
| #27163118 | 2 |
| #27163115 | 2 |
| D8×D397 | 2 |
| #27163102 | 2 |
| C2×D8×C397 | 2 |
| #576 | 397 |