Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
880 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11752051 | C2 | semidirect |
| 3. #11746786 | C2 | semidirect |
| 4. C3×#64915 | C2 | semidirect |
| 5. #11746567 | C2 | semidirect |
| 17. #91241 | C22 | semidirect |
| 18. C3×C22⋊#170 | C22 | semidirect |
| 25. #64915 | D3 | semidirect |
| 69. C22⋊#170 | C2×D3 | semidirect |
| 76. C22×D15 | M16 | semidirect |
| 87. C22×C3×D5 | M16 | semidirect |
| 233. C22×D5 | ΓL(1,𝔽25) | semidirect |
| 364. C3×C5 | #1462 | semidirect |
| 451. C5 | #68120 | semidirect |
| 481. C3 | #10604880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×#685 | 2 |
| #11752051 | 2 |
| #11746786 | 2 |
| C3×#64915 | 2 |
| #11746567 | 2 |
| #10604880 | 3 |
| #68120 | 5 |