Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 124 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. #10623904 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 4. #10623755 | C2 | semidirect |
| 5. C3⋊D3×#168 | C2 | semidirect |
| 14. C3⋊(C3⋊#168) | C22 | semidirect |
| 15. C32×#168 | C22 | semidirect |
| 19. C3×#681 | D3 | semidirect |
| 44. C3×#168 | C2×D3 | semidirect |
| 49. C5×C3⋊D3 | M16 | semidirect |
| 53. #681 | C3⋊D3 | direct (N × H) |
| 77. C32×C5 | C2×M16 | semidirect |
| 86. #168 | C2×C3⋊D3 | semidirect |
| 120. C3⋊D3 | #681 | direct (N × H) |
| 126. C3×C5 | D3×M16 | semidirect |
| 139. C32 | C2×#681 | semidirect |
| 153. C5 | M16×C3⋊D3 | semidirect |
| 162. C3 | D3×#681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| #10623904 | 2 |
| C32×#681 | 2 |
| #10623755 | 2 |
| C3⋊D3×#168 | 2 |
| D3×#681 | 3 |
| M16×C3⋊D3 | 5 |