Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11754011 | C2 | semidirect |
| 2. C5×#4908 | C2 | semidirect |
| 3. #11748090 | C2 | semidirect |
| 4. C2×#90941 | C2 | semidirect |
| 5. #11746336 | C2 | semidirect |
| 6. C3×#64737 | C2 | semidirect |
| 7. #11745905 | C2 | semidirect |
| 32. #64737 | D3 | semidirect |
| 63. #4908 | D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #69268 | semidirect |
| 357. C3 | #10602311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754011 | 2 |
| C5×#4908 | 2 |
| #11748090 | 2 |
| C2×#90941 | 2 |
| #11746336 | 2 |
| C3×#64737 | 2 |
| #11745905 | 2 |
| #10602311 | 3 |
| #69268 | 5 |