Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 372 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. #10624283 | C2 | semidirect |
| 2. C5×#3828 | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. #10623768 | C2 | semidirect |
| 5. #10623765 | C2 | semidirect |
| 6. #10623764 | C2 | semidirect |
| 7. #10623759 | C2 | semidirect |
| 23. C2×C3×#168 | D3 | semidirect |
| 37. #3828 | D5 | semidirect |
| 65. C2×#168 | C3⋊D3 | semidirect |
| 91. C32×C5 | #135 | semidirect |
| 144. C3×C5 | #904 | semidirect |
| 156. C32 | #4096 | semidirect |
| 172. C5 | #64113 | semidirect |
| 180. C3 | #91303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624283 | 2 |
| C5×#3828 | 2 |
| C2×C32×#168 | 2 |
| #10623768 | 2 |
| #10623765 | 2 |
| #10623764 | 2 |
| #10623759 | 2 |
| #91303 | 3 |
| #64113 | 5 |