Finite Group DatabasebetaFinite Group DatabasebetaOrder 52800.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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. D13200 | C2 | semidirect |
| 15. C3×C11×C25×C32 | C2 | semidirect |
| 17. C11×C25×C32 | D3 | semidirect |
| 22. C3×C25×C32 | D11 | semidirect |
| 38. C3×C11×C32 | D25 | semidirect |
| 42. C3×C11×C25 | D32 | semidirect |
| 44. C25×C32 | D33 | semidirect |
| 61. C11×C32 | D75 | semidirect |
| 67. C11×C25 | D96 | semidirect |
| 93. C3×C32 | D275 | semidirect |
| 98. C3×C25 | D352 | semidirect |
| 113. C3×C11 | D800 | semidirect |
| 115. C32 | D825 | semidirect |
| 118. C25 | D1056 | semidirect |
| 130. C11 | D2400 | semidirect |
| 140. C3 | D8800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13200 | 2 |
| D8800 | 3 |
| D5280 | 5 |
| D2400 | 11 |
| C3×C11×C25×C32 | 2 |