Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 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. #11747851 | C2 | semidirect |
| 4. #11746324 | C2 | semidirect |
| 6. C3×C16×Dic5 | C2 | semidirect |
| 7. #11745942 | C2 | semidirect |
| 20. #90944 | C4 | semidirect |
| 27. C16×Dic5 | D3 | semidirect |
| 35. Dic60 | C2×C4 | semidirect |
| 45. C3×#672 | C2×C4 | semidirect |
| 109. #672 | C4×D3 | semidirect |
| 126. C3×Dic5 | SD32 | semidirect |
| 201. Dic5 | #800 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 254. C5 | C4×#800 | semidirect |
| 266. C3 | #10599968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11747851 | 2 |
| Dic5×D24 | 2 |
| C2×#90944 | 2 |
| #11746324 | 2 |
| C5×#4509 | 2 |
| C3×C16×Dic5 | 2 |
| #11745942 | 2 |
| #10599968 | 3 |
| C4×#800 | 5 |