Finite Group DatabasebetaFinite Group DatabasebetaOrder 14400.
153 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 57 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. D3600 | C2 | semidirect |
| 6. C9×C25×C32 | C2 | semidirect |
| 20. C25×C32 | D9 | semidirect |
| 38. C9×C32 | D25 | semidirect |
| 41. C9×C25 | D32 | semidirect |
| 79. C32 | D225 | semidirect |
| 82. C25 | D288 | semidirect |
| 96. C9 | D800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3600 | 2 |
| D2400 | 3 |
| D1440 | 5 |
| C9×C25×C32 | 2 |