Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. Q16×Dic15 | C2 | semidirect |
| 3. C2×C3×#3961 | C2 | semidirect |
| 5. #11745928 | C2 | semidirect |
| 6. #11745898 | C2 | semidirect |
| 25. C2×#3961 | D3 | semidirect |
| 238. C3×C5 | #2211 | semidirect |
| 274. C5 | #71498 | semidirect |
| 286. C3 | #10602271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic15 | 2 |
| C2×C5×#828 | 2 |
| C2×C3×#3961 | 2 |
| #11747982 | 2 |
| #11745928 | 2 |
| #11745898 | 2 |
| #11745894 | 2 |
| #10602271 | 3 |
| #71498 | 5 |