Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 85. C3×C5×C8 | Q16 | semidirect |
| 170. C5×C8 | #216 | semidirect |
| 203. C3×C8 | Dic20 | semidirect |
| 234. C3×C5 | #1672 | semidirect |
| 264. C8 | #6662 | semidirect |
| 268. C5 | #71348 | semidirect |
| 279. C3 | #10599340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic30 | 2 |
| C3×#64969 | 2 |
| #11747104 | 2 |
| #11746917 | 2 |
| C5×#4457 | 2 |
| #11745861 | 2 |
| #11745856 | 2 |
| #10599340 | 3 |
| #71348 | 5 |