Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 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. C2×#20263731 | C2 | semidirect |
| 2. #27163127 | C2 | semidirect |
| 3. #27163126 | C2 | semidirect |
| 4. #27163122 | C2 | semidirect |
| 5. #27163121 | C2 | semidirect |
| 6. #27163116 | C2 | semidirect |
| 7. C2×#20263715 | C2 | semidirect |
| 8. C2×#41×C397 | C2 | semidirect |
| 12. #20263731 | C22 | semidirect |
| 13. C2×Dic794 | C22 | semidirect |
| 14. C2×D1588 | C22 | semidirect |
| 17. #20263721 | C22 | semidirect |
| 18. #20263719 | C22 | semidirect |
| 19. #20263718 | C22 | semidirect |
| 20. #20263716 | C22 | semidirect |
| 21. #20263715 | C22 | semidirect |
| 22. #20263715 | C22 | semidirect |
| 23. C2×#15691787 | C22 | semidirect |
| 27. #41×C397 | C22 | semidirect |
| 28. C2×Q8×C397 | C22 | semidirect |
| 30. C2×D4×C397 | C22 | semidirect |
| 81. C397 | #575 | semidirect |
| 84. C2×#41 | D397 | semidirect |
| 98. #41 | C2×D397 | semidirect |
| 100. C2×Q8 | C2×D397 | semidirect |
| 104. C2×D4 | C2×D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263731 | 2 |
| #27163127 | 2 |
| #27163126 | 2 |
| #27163122 | 2 |
| #27163121 | 2 |
| #27163116 | 2 |
| C2×#20263715 | 2 |
| C2×#41×C397 | 2 |
| #575 | 397 |