Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D401 |
| commutator, socle, cosocle | C22×C401 | C24 |
| Fitting | #121×C401 | C2 |
| hypercenter | #121 | D401 |
| hypocenter | C401 | #535 |
| LCS | G ▷ C22×C401 ▷ C401 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20264366 | C2 | semidirect |
| 2. C2×D4×D401 | C2 | semidirect |
| 3. #27165733 | C2 | semidirect |
| 4. #27165723 | C2 | semidirect |
| 5. #27165712 | C2 | semidirect |
| 6. #27165711 | C2 | semidirect |
| 7. #27165708 | C2 | semidirect |
| 8. #27165707 | C2 | semidirect |
| 9. #27165705 | C2 | semidirect |
| 10. #27165695 | C2 | semidirect |
| 11. #121×C401 | C2 | semidirect |
| 14. C2×Dic802 | C22 | semidirect |
| 17. C2×D1604 | C22 | semidirect |
| 20. C2×C22⋊D401 | C22 | semidirect |
| 21. C2×C22⋊D401 | C22 | semidirect |
| 22. C2×C22⋊D401 | C22 | semidirect |
| 25. C2×C4×D401 | C22 | semidirect |
| 26. C4⋊Dic401 | C22 | semidirect |
| 27. C22⋊Dic401 | C22 | semidirect |
| 29. #20264343 | C22 | semidirect |
| 30. #20264343 | C22 | semidirect |
| 31. C4×Dic401 | C22 | semidirect |
| 33. C2×D4×C401 | C22 | semidirect |
| 34. C22×C4×C401 | C22 | semidirect |
| 35. C4⋊C4×C401 | C22 | semidirect |
| 36. C22⋊C4×C401 | C22 | semidirect |
| 56. C4×D401 | D4 | semidirect |
| 96. C401 | #535 | semidirect |
| 105. #121 | D401 | semidirect |
| 122. C2×D4 | C2×D401 | semidirect |
| 125. C22×C4 | C2×D401 | semidirect |
| 127. C4⋊C4 | C2×D401 | semidirect |
| 132. C22⋊C4 | 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 |
| C2×D4×D401 | 2 |
| #27165733 | 2 |
| #27165723 | 2 |
| #27165712 | 2 |
| #27165711 | 2 |
| #27165708 | 2 |
| #27165707 | 2 |
| #27165705 | 2 |
| #27165695 | 2 |
| #121×C401 | 2 |
| #535 | 401 |