Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 94 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. #11747766 | C2 | semidirect |
| 2. Dic5×D24 | C2 | semidirect |
| 4. #11746330 | C2 | semidirect |
| 5. C5×#4509 | C2 | semidirect |
| 6. C3×C16×Dic5 | C2 | semidirect |
| 7. #11745939 | C2 | semidirect |
| 20. #90939 | C4 | semidirect |
| 27. C16×Dic5 | D3 | semidirect |
| 36. D120 | C2×C4 | semidirect |
| 39. C5×D24 | C2×C4 | semidirect |
| 45. C3×#672 | C2×C4 | semidirect |
| 51. #4509 | D5 | semidirect |
| 110. #672 | C4×D3 | semidirect |
| 129. C3×Dic5 | D16 | semidirect |
| 145. D24 | C4×D5 | semidirect |
| 209. Dic5 | D48 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 267. C5 | C4×D48 | semidirect |
| 281. C3 | #10599967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11747766 | 2 |
| Dic5×D24 | 2 |
| C2×#90939 | 2 |
| #11746330 | 2 |
| C5×#4509 | 2 |
| C3×C16×Dic5 | 2 |
| #11745939 | 2 |
| #10599967 | 3 |
| C4×D48 | 5 |