Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
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×D401 | C2 | semidirect |
| 2. #27165769 | C2 | semidirect |
| 3. #27165766 | C2 | semidirect |
| 4. #27165764 | C2 | semidirect |
| 5. #27165761 | C2 | semidirect |
| 6. #27165759 | C2 | semidirect |
| 7. #27165757 | C2 | semidirect |
| 8. C2×#20264349 | C2 | semidirect |
| 9. #135×C401 | C2 | semidirect |
| 12. #20264366 | C22 | semidirect |
| 15. Q8×D401 | C22 | semidirect |
| 17. D4×D401 | C22 | semidirect |
| 20. Dic1604 | C22 | semidirect |
| 21. #20264356 | C22 | semidirect |
| 22. #20264355 | C22 | semidirect |
| 23. #20264354 | C22 | semidirect |
| 24. #20264353 | C22 | semidirect |
| 25. D3208 | C22 | semidirect |
| 26. #20264351 | C22 | semidirect |
| 27. #20264349 | C22 | semidirect |
| 28. #20264349 | C22 | semidirect |
| 29. C2×#15691999 | C22 | semidirect |
| 30. #41×C401 | C22 | semidirect |
| 31. Q16×C401 | C22 | semidirect |
| 32. SD16×C401 | C22 | semidirect |
| 33. D8×C401 | C22 | semidirect |
| 34. C2×C8×C401 | C22 | semidirect |
| 75. C401 | #575 | semidirect |
| 84. #135 | D401 | semidirect |
| 91. #41 | C2×D401 | semidirect |
| 99. Q16 | C2×D401 | semidirect |
| 103. SD16 | C2×D401 | semidirect |
| 106. D8 | C2×D401 | semidirect |
| 110. C2×C8 | C2×D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D401 | 2 |
| #27165769 | 2 |
| #27165766 | 2 |
| #27165764 | 2 |
| #27165761 | 2 |
| #27165759 | 2 |
| #27165757 | 2 |
| C2×#20264349 | 2 |
| #135×C401 | 2 |
| #575 | 401 |