Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11747529 | C2 | semidirect |
| 3. #11747525 | C2 | semidirect |
| 4. #11746323 | C2 | semidirect |
| 5. C5×#4508 | C2 | semidirect |
| 6. C3×#64728 | C2 | semidirect |
| 7. #11745931 | C2 | semidirect |
| 30. #64728 | D3 | semidirect |
| 57. #4508 | D5 | semidirect |
| 240. C3×C5 | #2171 | semidirect |
| 273. C5 | #69123 | semidirect |
| 282. C3 | #10599916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11748074 | 2 |
| #11747529 | 2 |
| #11747525 | 2 |
| #11746323 | 2 |
| C5×#4508 | 2 |
| C3×#64728 | 2 |
| #11745931 | 2 |
| #10599916 | 3 |
| #69123 | 5 |