Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 11. #91233 | C4 | semidirect |
| 12. C3×C4×C5×C8 | C4 | semidirect |
| 15. C3×C4×#168 | C4 | semidirect |
| 45. C4×C5×C8 | Dic3 | semidirect |
| 48. C4×#168 | Dic3 | semidirect |
| 75. C3×C4×C8 | AGL(1,𝔽5) | semidirect |
| 154. C4×C8 | ΓL(1,𝔽16) | semidirect |
| 210. C3×C5 | #1286 | semidirect |
| 254. C5 | #67738 | semidirect |
| 269. C3 | #10598527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752348 | 2 |
| #11752341 | 2 |
| C3×#64974 | 2 |
| #10598527 | 3 |
| #67738 | 5 |