Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 56. C3×C5×Q8 | Q16 | semidirect |
| 123. C5×Q8 | Dic12 | semidirect |
| 151. C3×Q8 | Dic20 | semidirect |
| 187. C3×C5 | #1670 | semidirect |
| 203. Q8 | Dic60 | semidirect |
| 217. C5 | #70942 | semidirect |
| 227. C3 | #10601735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C8×Q8 | 2 |
| #11751121 | 2 |
| #11750800 | 2 |
| #11746303 | 2 |
| #11746279 | 2 |
| #10601735 | 3 |
| #70942 | 5 |