Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
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×#20264366 | C2 | semidirect |
| 2. #27165768 | C2 | semidirect |
| 3. #27165767 | C2 | semidirect |
| 4. #27165763 | C2 | semidirect |
| 5. #27165762 | C2 | semidirect |
| 6. #27165757 | C2 | semidirect |
| 7. C2×#20264350 | C2 | semidirect |
| 8. C2×#41×C401 | C2 | semidirect |
| 12. #20264366 | C22 | semidirect |
| 13. C2×Dic802 | C22 | semidirect |
| 14. C2×D1604 | C22 | semidirect |
| 17. #20264356 | C22 | semidirect |
| 18. #20264354 | C22 | semidirect |
| 19. #20264353 | C22 | semidirect |
| 20. #20264351 | C22 | semidirect |
| 21. #20264350 | C22 | semidirect |
| 22. #20264350 | C22 | semidirect |
| 23. C2×#15691999 | C22 | semidirect |
| 27. #41×C401 | C22 | semidirect |
| 28. C2×Q8×C401 | C22 | semidirect |
| 30. C2×D4×C401 | C22 | semidirect |
| 81. C401 | #575 | semidirect |
| 84. C2×#41 | D401 | semidirect |
| 98. #41 | C2×D401 | semidirect |
| 100. C2×Q8 | C2×D401 | semidirect |
| 104. C2×D4 | C2×D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20264366 | 2 |
| #27165768 | 2 |
| #27165767 | 2 |
| #27165763 | 2 |
| #27165762 | 2 |
| #27165757 | 2 |
| C2×#20264350 | 2 |
| C2×#41×C401 | 2 |
| #575 | 401 |