Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×C3×#3930 | C2 | semidirect |
| 3. C2×#90935 | C2 | semidirect |
| 4. #11746322 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 6. #11745879 | C2 | semidirect |
| 7. #11745872 | C2 | semidirect |
| 25. C2×#3930 | D3 | semidirect |
| 47. C3×#672 | D4 | semidirect |
| 53. (C2×D3)⋊C16 | D5 | semidirect |
| 118. #672 | #67 | semidirect |
| 136. Dic15 | M32 | semidirect |
| 242. C3×C5 | #2169 | semidirect |
| 283. C5 | #71430 | semidirect |
| 297. C3 | #10599897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3930 | 2 |
| C8×#1201 | 2 |
| C2×#90935 | 2 |
| #11746322 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| #11745879 | 2 |
| #11745872 | 2 |
| #10599897 | 3 |
| #71430 | 5 |