Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10624196 | C2 | semidirect |
| 2. #10624194 | C2 | semidirect |
| 3. C8×C3⋊D15 | C2 | semidirect |
| 4. C3×#6706 | C2 | semidirect |
| 5. C3×C5×#204 | C2 | semidirect |
| 6. #10623807 | C2 | semidirect |
| 7. #10623798 | C2 | semidirect |
| 29. #6706 | D3 | semidirect |
| 33. C5×#204 | D3 | semidirect |
| 49. C3×#204 | D5 | semidirect |
| 129. #204 | D15 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 207. C3×C5 | #916 | semidirect |
| 208. C3×C5 | #916 | semidirect |
| 230. C32 | #4062 | semidirect |
| 252. C5 | #63809 | semidirect |
| 261. C3 | #91276 | semidirect |
| 262. C3 | #91805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624196 | 2 |
| #10624194 | 2 |
| C8×C3⋊D15 | 2 |
| C3×#6706 | 2 |
| C3×C5×#204 | 2 |
| #10623807 | 2 |
| #10623798 | 2 |
| #91805 | 3 |
| #91276 | 3 |
| #63809 | 5 |