Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 50 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. #11751020 | C2 | semidirect |
| 2. #11746842 | C2 | semidirect |
| 3. C5×#4521 | C2 | semidirect |
| 4. C3×#64742 | C2 | semidirect |
| 5. #11745824 | C2 | semidirect |
| 6. #11745820 | C2 | semidirect |
| 7. #11745814 | C2 | semidirect |
| 24. #64742 | D3 | semidirect |
| 43. #4521 | D5 | semidirect |
| 171. C3×C5 | #2262 | semidirect |
| 198. C5 | #69383 | semidirect |
| 206. C3 | #10600172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751020 | 2 |
| #11746842 | 2 |
| C5×#4521 | 2 |
| C3×#64742 | 2 |
| #11745824 | 2 |
| #11745820 | 2 |
| #11745814 | 2 |
| #10600172 | 3 |
| #69383 | 5 |