Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11750797 | C2 | semidirect |
| 2. C4×C5×D24 | C2 | semidirect |
| 3. C2×#90944 | C2 | semidirect |
| 5. C3×C4⋊#672 | C2 | semidirect |
| 6. #11745902 | C2 | semidirect |
| 7. #11745896 | C2 | semidirect |
| 29. C4⋊#672 | D3 | semidirect |
| 53. C4×D24 | D5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #69288 | semidirect |
| 301. C3 | #10601683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750797 | 2 |
| C4×C5×D24 | 2 |
| C2×#90944 | 2 |
| C2×#90939 | 2 |
| C3×C4⋊#672 | 2 |
| #11745902 | 2 |
| #11745896 | 2 |
| #10601683 | 3 |
| #69288 | 5 |