Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11751177 | C2 | semidirect |
| 3. #11750947 | C2 | semidirect |
| 4. #11750939 | C2 | semidirect |
| 5. C3×C5×#331 | C2 | semidirect |
| 6. #11746303 | C2 | semidirect |
| 7. #11746300 | C2 | semidirect |
| 29. C5×#331 | D3 | semidirect |
| 56. C3×#331 | D5 | semidirect |
| 97. C3⋊#168 | D8 | semidirect |
| 139. #331 | D15 | semidirect |
| 274. C3×C5 | #1685 | semidirect |
| 322. C5 | #68398 | semidirect |
| 337. C3 | #10599191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751177 | 2 |
| #11751173 | 2 |
| #11750947 | 2 |
| #11750939 | 2 |
| C3×C5×#331 | 2 |
| #11746303 | 2 |
| #11746300 | 2 |
| #10599191 | 3 |
| #68398 | 5 |