Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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. #41×D397 | C2 | semidirect |
| 2. #27163128 | C2 | semidirect |
| 3. #27163125 | C2 | semidirect |
| 4. #27163123 | C2 | semidirect |
| 5. #27163120 | C2 | semidirect |
| 6. #27163118 | C2 | semidirect |
| 7. #27163116 | C2 | semidirect |
| 8. C2×#20263714 | C2 | semidirect |
| 9. #135×C397 | C2 | semidirect |
| 12. #20263731 | C22 | semidirect |
| 15. Q8×D397 | C22 | semidirect |
| 17. D4×D397 | C22 | semidirect |
| 20. Dic1588 | C22 | semidirect |
| 21. #20263721 | C22 | semidirect |
| 22. #20263720 | C22 | semidirect |
| 23. #20263719 | C22 | semidirect |
| 24. #20263718 | C22 | semidirect |
| 25. D3176 | C22 | semidirect |
| 26. #20263716 | C22 | semidirect |
| 27. #20263714 | C22 | semidirect |
| 28. #20263714 | C22 | semidirect |
| 29. C2×#15691787 | C22 | semidirect |
| 30. #41×C397 | C22 | semidirect |
| 31. Q16×C397 | C22 | semidirect |
| 32. SD16×C397 | C22 | semidirect |
| 33. D8×C397 | C22 | semidirect |
| 34. C2×C8×C397 | C22 | semidirect |
| 75. C397 | #575 | semidirect |
| 84. #135 | D397 | semidirect |
| 91. #41 | C2×D397 | semidirect |
| 99. Q16 | C2×D397 | semidirect |
| 103. SD16 | C2×D397 | semidirect |
| 106. D8 | C2×D397 | semidirect |
| 110. C2×C8 | C2×D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D397 | 2 |
| #27163128 | 2 |
| #27163125 | 2 |
| #27163123 | 2 |
| #27163120 | 2 |
| #27163118 | 2 |
| #27163116 | 2 |
| C2×#20263714 | 2 |
| #135×C397 | 2 |
| #575 | 397 |