Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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. C4×C3⋊Dic15 | C2 | semidirect |
| 3. C32×#683 | C2 | semidirect |
| 4. #10623775 | C2 | semidirect |
| 5. #10623773 | C2 | semidirect |
| 19. C3×#683 | D3 | semidirect |
| 59. #683 | C3⋊D3 | semidirect |
| 85. C32×C5 | #126 | semidirect |
| 136. C3×C5 | #898 | semidirect |
| 151. C32 | #4025 | semidirect |
| 163. C5 | #64107 | semidirect |
| 174. C3 | #91367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊Dic15 | 2 |
| C5×#3752 | 2 |
| C32×#683 | 2 |
| #10623775 | 2 |
| #10623773 | 2 |
| #10623771 | 2 |
| #91367 | 3 |
| #64107 | 5 |