Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11748037 | C2 | semidirect |
| 3. #11746322 | C2 | semidirect |
| 5. C3×#64725 | C2 | semidirect |
| 6. #11745943 | C2 | semidirect |
| 25. #64725 | D3 | semidirect |
| 36. C5×D24 | Q8 | semidirect |
| 132. D24 | Dic10 | semidirect |
| 204. C3×C5 | #2226 | semidirect |
| 238. C5 | #69353 | semidirect |
| 250. C3 | #10599972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11748037 | 2 |
| #11747810 | 2 |
| #11746322 | 2 |
| C5×#4509 | 2 |
| C3×#64725 | 2 |
| #11745943 | 2 |
| #11745893 | 2 |
| #10599972 | 3 |
| #69353 | 5 |