Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
264 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 9. #91222 | C4 | semidirect |
| 11. C3×#3993 | C4 | semidirect |
| 12. C2×C3⋊#672 | C4 | semidirect |
| 13. C2×C5×C3⋊C16 | C4 | semidirect |
| 44. #3993 | Dic3 | semidirect |
| 73. C2×C3⋊C16 | AGL(1,𝔽5) | semidirect |
| 183. C3×C5 | #1384 | semidirect |
| 215. C5 | #67725 | semidirect |
| 226. C3 | #10598666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752380 | 2 |
| C3×#65721 | 2 |
| C2×#90934 | 2 |
| #10598666 | 3 |
| #67725 | 5 |