Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×D3×Dic20 | C2 | semidirect |
| 2. C2×C3×#3932 | C2 | semidirect |
| 4. C2×#90942 | C2 | semidirect |
| 5. #11746324 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 7. #11745898 | C2 | semidirect |
| 28. C2×#3932 | D3 | semidirect |
| 44. Dic60 | D4 | semidirect |
| 49. C3×Dic20 | D4 | semidirect |
| 61. (C2×D3)⋊C16 | D5 | semidirect |
| 134. Dic20 | #67 | semidirect |
| 149. C2×C5×D3 | SD32 | semidirect |
| 282. C3×C5 | #2185 | semidirect |
| 289. C2×D3 | #3932 | semidirect |
| 327. C5 | #71483 | semidirect |
| 341. C3 | #10599905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic20 | 2 |
| C2×C3×#3932 | 2 |
| #11747915 | 2 |
| C2×#90942 | 2 |
| #11746324 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| #11745898 | 2 |
| #10599905 | 3 |
| #71483 | 5 |