Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
800 conjugacy classes of subgroups; only the 316 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 316 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. C22×C5×C3⋊C16 | C2 | semidirect |
| 3. C22×C3×#672 | C2 | semidirect |
| 4. C2×#90936 | C2 | direct (N × H) |
| 11. C2×C5×C3⋊C16 | C22 | semidirect |
| 12. C2×C3×#672 | C22 | semidirect |
| 13. #90936 | C22 | direct (N × H) |
| 17. C22×#672 | D3 | semidirect |
| 29. C3×#672 | C23 | semidirect |
| 30. C5×C3⋊C16 | C23 | semidirect |
| 33. C22×C3⋊C16 | D5 | semidirect |
| 41. C2×#672 | C2×D3 | semidirect |
| 61. C2×C3⋊C16 | C2×D5 | semidirect |
| 74. #672 | C22×D3 | semidirect |
| 79. C22×C3×C5 | M32 | semidirect |
| 97. C3⋊C16 | C22×D5 | semidirect |
| 117. C2×C3×C5 | C2×M32 | semidirect |
| 131. C22×C5 | #798 | semidirect |
| 150. C3×C5 | C22×M32 | semidirect |
| 151. C22×C3 | #3930 | semidirect |
| 158. C2×C5 | C2×#798 | semidirect |
| 172. C2×C3 | C2×#3930 | semidirect |
| 175. C5 | C22×#798 | semidirect |
| 178. C22 | #90936 | direct (N × H) |
| 183. C3 | C22×#3930 | semidirect |
| 185. C2 | C2×#90936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D15 | 2 |
| C22×C5×C3⋊C16 | 2 |
| C22×C3×#672 | 2 |
| C2×#90936 | 2 |
| C22×#3930 | 3 |
| C22×#798 | 5 |