Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 332 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×#64969 | C2 | semidirect |
| 5. #11746278 | C2 | semidirect |
| 6. #11745861 | C2 | semidirect |
| 7. #11745855 | C2 | semidirect |
| 28. #64969 | D3 | semidirect |
| 88. C3×C5×C8 | SD16 | semidirect |
| 178. C5×C8 | #215 | semidirect |
| 215. C3×C8 | #687 | semidirect |
| 249. C3×C5 | #1671 | semidirect |
| 284. C8 | #6656 | semidirect |
| 289. C5 | #71344 | semidirect |
| 302. C3 | #10601644 | 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×#64969 | 2 |
| #11747070 | 2 |
| #11746882 | 2 |
| #11746278 | 2 |
| #11745861 | 2 |
| #11745855 | 2 |
| #10601644 | 3 |
| #71344 | 5 |