Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10624220 | C2 | semidirect |
| 2. C5×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×#6706 | C2 | semidirect |
| 4. #10623827 | C2 | semidirect |
| 5. #10623822 | C2 | semidirect |
| 17. #6706 | D3 | semidirect |
| 30. C8×C3⋊D3 | D5 | semidirect |
| 82. C32×C5 | #135 | semidirect |
| 130. C3×C5 | #916 | semidirect |
| 144. C32 | #4050 | semidirect |
| 158. C5 | #63809 | semidirect |
| 165. C3 | #91272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624220 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×#6706 | 2 |
| #10623827 | 2 |
| #10623822 | 2 |
| #91272 | 3 |
| #63809 | 5 |