Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
252 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 76 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. #11748027 | C2 | semidirect |
| 5. #11745935 | C2 | semidirect |
| 6. #11745934 | C2 | semidirect |
| 7. #11745932 | C2 | semidirect |
| 30. C3×C5×Q16 | Q8 | semidirect |
| 32. C3×C5×D8 | Q8 | semidirect |
| 90. C5×Q16 | Dic6 | semidirect |
| 92. C5×D8 | Dic6 | semidirect |
| 121. C3×Q16 | Dic10 | semidirect |
| 123. C3×D8 | Dic10 | semidirect |
| 187. Q16 | #1204 | semidirect |
| 189. D8 | #1204 | semidirect |
| 201. C3×C5 | #2230 | semidirect |
| 230. C5 | #69246 | semidirect |
| 239. C3 | #10601712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5196 | 2 |
| #11748027 | 2 |
| #11746387 | 2 |
| C3×#64786 | 2 |
| #11745935 | 2 |
| #11745934 | 2 |
| #11745932 | 2 |
| #10601712 | 3 |
| #69246 | 5 |