Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×#91227 | C2 | semidirect |
| 3. C22×C3×#674 | C2 | semidirect |
| 4. #11746547 | C2 | semidirect |
| 20. C22×#674 | D3 | semidirect |
| 206. C3×C5 | #2113 | semidirect |
| 240. C5 | #71409 | semidirect |
| 250. C3 | #10604742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91290 | 2 |
| C2×#91227 | 2 |
| C22×C3×#674 | 2 |
| #11746547 | 2 |
| #10604742 | 3 |
| #71409 | 5 |