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. C2×#67180 | C2 | semidirect |
| 3. C32×#681 | C2 | semidirect |
| 4. #10623768 | C2 | semidirect |
| 5. #10623764 | C2 | semidirect |
| 19. C3×#681 | D3 | semidirect |
| 51. #681 | C3⋊D3 | semidirect |
| 72. C32×C5 | #137 | semidirect |
| 115. C3×C5 | #909 | semidirect |
| 125. C32 | #4097 | semidirect |
| 138. C5 | #64118 | semidirect |
| 145. C3 | #91322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C5×#3828 | 2 |
| C32×#681 | 2 |
| #10623768 | 2 |
| #10623764 | 2 |
| #91322 | 3 |
| #64118 | 5 |