Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C3×#3995 | C2 | semidirect |
| 3. #11751825 | C2 | semidirect |
| 6. #11746763 | C2 | semidirect |
| 7. #11746524 | C2 | semidirect |
| 24. #91100 | C4 | semidirect |
| 25. C5×#821 | C4 | semidirect |
| 26. #90975 | C4 | semidirect |
| 27. #90967 | C4 | semidirect |
| 31. C2×#3995 | D3 | semidirect |
| 137. #821 | AGL(1,𝔽5) | semidirect |
| 358. C3×C5 | #1866 | semidirect |
| 415. C5 | #70722 | semidirect |
| 432. C3 | #10603965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91913 | 2 |
| C2×C3×#3995 | 2 |
| #11751825 | 2 |
| C2×#91155 | 2 |
| #11748135 | 2 |
| #11746763 | 2 |
| #11746524 | 2 |
| #10603965 | 3 |
| #70722 | 5 |