Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
784 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 156 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. #11752631 | C2 | semidirect |
| 3. #11750808 | C2 | semidirect |
| 4. C5×#4713 | C2 | semidirect |
| 5. C3×#64992 | C2 | semidirect |
| 6. #11748146 | C2 | semidirect |
| 7. #11747979 | C2 | semidirect |
| 8. #11746925 | C2 | semidirect |
| 9. #11746905 | C2 | semidirect |
| 41. #64992 | D3 | semidirect |
| 73. #4713 | D5 | semidirect |
| 305. C3×C5 | #3142 | semidirect |
| 345. C5 | #81740 | semidirect |
| 358. C3 | #10613447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752631 | 2 |
| #11752559 | 2 |
| #11750808 | 2 |
| C5×#4713 | 2 |
| C3×#64992 | 2 |
| #11748146 | 2 |
| #11747979 | 2 |
| #11746925 | 2 |
| #11746905 | 2 |
| #10613447 | 3 |
| #81740 | 5 |