Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
420 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×#66100 | C2 | semidirect |
| 2. C2×#91112 | C2 | semidirect |
| 3. #11748082 | C2 | semidirect |
| 4. #11747544 | C2 | semidirect |
| 5. C5×#4565 | C2 | semidirect |
| 6. #11745903 | C2 | semidirect |
| 7. #11745885 | C2 | semidirect |
| 27. #66100 | D3 | semidirect |
| 66. #4565 | D5 | semidirect |
| 302. C3×C5 | #2193 | semidirect |
| 346. C5 | #72124 | semidirect |
| 357. C3 | #10600061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66100 | 2 |
| C2×#91112 | 2 |
| #11748082 | 2 |
| #11747544 | 2 |
| C5×#4565 | 2 |
| #11745903 | 2 |
| #11745885 | 2 |
| #10600061 | 3 |
| #72124 | 5 |