Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×#6758 | C2 | semidirect |
| 3. C32×D5⋊C8 | C2 | semidirect |
| 4. C3×#6739 | C2 | semidirect |
| 5. C3×D3×#170 | C2 | semidirect |
| 7. #91911 | C3 | direct (N × H) |
| 19. #6758 | C2×C3 | semidirect |
| 24. C3×D5⋊C8 | D3 | semidirect |
| 25. C3×D5⋊C8 | C2×C3 | semidirect |
| 26. #6739 | C2×C3 | semidirect |
| 27. D3×#170 | C2×C3 | semidirect |
| 67. D5⋊C8 | C3×D3 | semidirect |
| 100. C32×C5 | #131 | semidirect |
| 156. C3×C5 | #901 | semidirect |
| 157. C3×C5 | C3×#131 | semidirect |
| 174. C32 | #4131 | semidirect |
| 191. C5 | C3×#901 | semidirect |
| 198. C3 | #91911 | direct (N × H) |
| 199. C3 | C3×#4131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6772 | 2 |
| C3×#6758 | 2 |
| C32×D5⋊C8 | 2 |
| C3×#6739 | 2 |
| C3×D3×#170 | 2 |
| C3×#4131 | 3 |
| #91911 | 3 |
| C3×#901 | 5 |