Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
372 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 76 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. #11750973 | C2 | semidirect |
| 2. #11748012 | C2 | semidirect |
| 3. C2×#90939 | C2 | semidirect |
| 4. C2×#90938 | C2 | semidirect |
| 5. C5×#4491 | C2 | semidirect |
| 6. C3×#64711 | C2 | semidirect |
| 7. #11745928 | C2 | semidirect |
| 29. #64711 | D3 | semidirect |
| 42. D120 | D4 | semidirect |
| 56. #4491 | D5 | semidirect |
| 144. Dic15 | D16 | semidirect |
| 257. C3×C5 | #2206 | semidirect |
| 304. C5 | #69202 | semidirect |
| 320. C3 | #10599995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750973 | 2 |
| #11748012 | 2 |
| C2×#90939 | 2 |
| C2×#90938 | 2 |
| C5×#4491 | 2 |
| C3×#64711 | 2 |
| #11745928 | 2 |
| #10599995 | 3 |
| #69202 | 5 |