Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11751161 | C2 | semidirect |
| 3. #11751156 | C2 | semidirect |
| 4. #11746361 | C2 | semidirect |
| 5. #11746361 | C2 | semidirect |
| 15. #91758 | C22 | semidirect |
| 18. #91087 | C22 | semidirect |
| 19. #91087 | C22 | semidirect |
| 241. C3×C5 | #1659 | semidirect |
| 281. C5 | #71949 | semidirect |
| 294. C3 | #10602742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×H(3,𝔽4) | 2 |
| #11751161 | 2 |
| #11751156 | 2 |
| #11746361 | 2 |
| #10602742 | 3 |
| #71949 | 5 |