Finite Group DatabasebetaFinite Group DatabasebetaOrder 31200.
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 27. C3×C13×C25 | Q32 | semidirect |
| 43. C13×C25 | Dic24 | semidirect |
| 72. C3×C25 | Dic104 | semidirect |
| 83. C3×C13 | Dic200 | semidirect |
| 87. C25 | Dic312 | semidirect |
| 95. C13 | Dic600 | semidirect |
| 105. C3 | Dic2600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3900 | 2 |
| Dic2600 | 3 |
| Dic1560 | 5 |
| Dic600 | 13 |
| C3×C13×C16×C25 | 2 |