Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 268 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. #10624224 | C2 | semidirect |
| 2. #10624221 | C2 | semidirect |
| 3. C5×#3744 | C2 | semidirect |
| 4. C3×#6706 | C2 | semidirect |
| 5. C3×C8×D15 | C2 | semidirect |
| 6. #10623826 | C2 | semidirect |
| 7. #10623821 | C2 | semidirect |
| 26. #6706 | D3 | semidirect |
| 27. C8×D15 | D3 | semidirect |
| 47. #3744 | D5 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #904 | semidirect |
| 208. C3×C5 | #916 | semidirect |
| 230. C32 | #4062 | semidirect |
| 252. C5 | #63806 | semidirect |
| 261. C3 | #91269 | semidirect |
| 262. C3 | #91276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624224 | 2 |
| #10624221 | 2 |
| C5×#3744 | 2 |
| C3×#6706 | 2 |
| C3×C8×D15 | 2 |
| #10623826 | 2 |
| #10623821 | 2 |
| #91276 | 3 |
| #91269 | 3 |
| #63806 | 5 |