Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 3. C2×#91234 | C2 | semidirect |
| 4. C2×C3×#4005 | C2 | semidirect |
| 6. #11746576 | C2 | semidirect |
| 7. #11746575 | C2 | semidirect |
| 37. C2×#4005 | D3 | semidirect |
| 471. C3×C5 | #1915 | semidirect |
| 541. C5 | #70124 | semidirect |
| 560. C3 | #10604536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756863 | 2 |
| #11754317 | 2 |
| C2×#91234 | 2 |
| C2×C3×#4005 | 2 |
| #11752008 | 2 |
| #11746576 | 2 |
| #11746575 | 2 |
| #10604536 | 3 |
| #70124 | 5 |