Finite Group DatabasebetaFinite Group DatabasebetaOrder 50400.
252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 93 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. D12600 | C2 | semidirect |
| 16. C7×C9×C16×C25 | C2 | semidirect |
| 21. C9×C16×C25 | D7 | semidirect |
| 22. C7×C16×C25 | D9 | semidirect |
| 34. C7×C9×C25 | D16 | semidirect |
| 46. C7×C9×C16 | D25 | semidirect |
| 72. C16×C25 | D63 | semidirect |
| 89. C9×C25 | D112 | semidirect |
| 97. C7×C25 | D144 | semidirect |
| 104. C9×C16 | D175 | semidirect |
| 112. C7×C16 | D225 | semidirect |
| 128. C7×C9 | D400 | semidirect |
| 150. C25 | D1008 | semidirect |
| 159. C16 | D1575 | semidirect |
| 167. C9 | D2800 | semidirect |
| 170. C7 | D3600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D12600 | 2 |
| D8400 | 3 |
| D5040 | 5 |
| D3600 | 7 |
| C7×C9×C16×C25 | 2 |