Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 3. C5×#4461 | C2 | semidirect |
| 4. C3×#64681 | C2 | semidirect |
| 5. #11745872 | C2 | semidirect |
| 16. #90936 | C4 | semidirect |
| 22. #64681 | D3 | semidirect |
| 34. C3×#672 | C2×C4 | semidirect |
| 35. C5×C3⋊C16 | C2×C4 | semidirect |
| 40. #4461 | D5 | semidirect |
| 86. #672 | C4×D3 | semidirect |
| 99. Dic15 | M32 | semidirect |
| 112. C3⋊C16 | C4×D5 | semidirect |
| 171. C3×C5 | C4×M32 | semidirect |
| 198. C5 | #69071 | semidirect |
| 207. C3 | #10599864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×D15 | 2 |
| C2×#90936 | 2 |
| C5×#4461 | 2 |
| C3×#64681 | 2 |
| #11745872 | 2 |
| #10599864 | 3 |
| #69071 | 5 |