Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. #11748019 | C2 | semidirect |
| 5. #11745944 | C2 | semidirect |
| 6. #11745943 | C2 | semidirect |
| 7. #11745927 | C2 | semidirect |
| 32. C3×C5×D8 | Q8 | semidirect |
| 91. C5×D8 | Dic6 | semidirect |
| 124. C3×D8 | Dic10 | semidirect |
| 193. D8 | #1204 | semidirect |
| 204. C3×C5 | #2226 | semidirect |
| 238. C5 | #70887 | semidirect |
| 250. C3 | #10599972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D8×Dic5 | 2 |
| #11748019 | 2 |
| #11746383 | 2 |
| C5×#4562 | 2 |
| #11745944 | 2 |
| #11745943 | 2 |
| #11745927 | 2 |
| #10599972 | 3 |
| #70887 | 5 |