Finite Group DatabasebetaFinite Group DatabasebetaOrder 25200.
162 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 162 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 |
|---|---|---|
| 19. C7×C9×C25 | Q16 | semidirect |
| 57. C9×C25 | Dic28 | semidirect |
| 63. C7×C25 | Dic36 | semidirect |
| 85. C7×C9 | Dic100 | semidirect |
| 102. C25 | Dic252 | semidirect |
| 115. C9 | Dic700 | semidirect |
| 118. C7 | Dic900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3150 | 2 |
| Dic2100 | 3 |
| Dic1260 | 5 |
| Dic900 | 7 |
| C7×C8×C9×C25 | 2 |