Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
664 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11756822 | C2 | semidirect |
| 3. #11751816 | C2 | semidirect |
| 4. #11751719 | C2 | semidirect |
| 5. #11751718 | C2 | semidirect |
| 6. #11746733 | C2 | semidirect |
| 7. C3×#64862 | C2 | semidirect |
| 18. #91758 | C4 | semidirect |
| 19. C5×#874 | C4 | semidirect |
| 23. #91373 | C4 | semidirect |
| 24. #91373 | C4 | semidirect |
| 35. #64862 | D3 | semidirect |
| 59. #6758 | D4 | semidirect |
| 65. C3×#700 | D4 | semidirect |
| 150. #874 | AGL(1,𝔽5) | semidirect |
| 186. #700 | D12 | semidirect |
| 411. C3×C5 | #1884 | semidirect |
| 477. C5 | #68777 | semidirect |
| 496. C3 | #10604618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756822 | 2 |
| #11752672 | 2 |
| #11751816 | 2 |
| #11751719 | 2 |
| #11751718 | 2 |
| #11746733 | 2 |
| C3×#64862 | 2 |
| #10604618 | 3 |
| #68777 | 5 |