Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C3×#64971 | C2 | semidirect |
| 4. #11746279 | C2 | semidirect |
| 5. #11745855 | C2 | semidirect |
| 21. #64971 | D3 | semidirect |
| 68. C3×C5×C8 | SD16 | semidirect |
| 140. C5×C8 | #215 | semidirect |
| 170. C3×C8 | #687 | semidirect |
| 198. C3×C5 | #1673 | semidirect |
| 229. C8 | #6656 | semidirect |
| 234. C5 | #71371 | semidirect |
| 246. C3 | #10601645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C8×D12 | 2 |
| C3×#64971 | 2 |
| #11747070 | 2 |
| #11746279 | 2 |
| #11745855 | 2 |
| #10601645 | 3 |
| #71371 | 5 |