Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
444 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 96 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. C3×#65708 | C2 | semidirect |
| 4. C2×#91150 | C2 | semidirect |
| 6. #11746746 | C2 | semidirect |
| 7. #11746532 | C2 | semidirect |
| 22. #91094 | C4 | semidirect |
| 23. C5×#809 | C4 | semidirect |
| 24. #90974 | C4 | semidirect |
| 25. #90966 | C4 | semidirect |
| 30. #65708 | D3 | semidirect |
| 133. #809 | AGL(1,𝔽5) | semidirect |
| 342. C3×C5 | #1938 | semidirect |
| 399. C5 | #70536 | semidirect |
| 416. C3 | #10603956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65708 | 2 |
| #11751801 | 2 |
| C2×#91155 | 2 |
| C2×#91150 | 2 |
| #11747499 | 2 |
| #11746746 | 2 |
| #11746532 | 2 |
| #10603956 | 3 |
| #70536 | 5 |