Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 2. C22×C32×Dic5 | C2 | semidirect |
| 3. C2×#67137 | C2 | semidirect |
| 4. C5×#3757 | C2 | semidirect |
| 5. #10623774 | C2 | semidirect |
| 6. #10623772 | C2 | semidirect |
| 7. Dic5×C3⋊Dic3 | C2 | semidirect |
| 11. #67184 | C4 | semidirect |
| 21. C22×C3×Dic5 | D3 | semidirect |
| 29. C22×C32×C5 | C2×C4 | semidirect |
| 33. C2×C3⋊D15 | C2×C4 | semidirect |
| 34. C3⋊Dic15 | C2×C4 | semidirect |
| 38. C32×Dic5 | D4 | semidirect |
| 43. #3757 | D5 | semidirect |
| 64. C22×Dic5 | C3⋊D3 | semidirect |
| 82. C22×C3×C5 | C4×D3 | semidirect |
| 89. C3×Dic5 | #67 | semidirect |
| 99. C32×C5 | C4×D4 | semidirect |
| 112. C22×C32 | C4×D5 | semidirect |
| 140. C22×C5 | C4×C3⋊D3 | semidirect |
| 149. Dic5 | #638 | semidirect |
| 162. C3×C5 | C4×#67 | semidirect |
| 165. C22×C3 | #1200 | semidirect |
| 180. C32 | #4027 | semidirect |
| 196. C5 | C4×#638 | semidirect |
| 202. C22 | #67137 | semidirect |
| 209. C3 | #91552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67184 | 2 |
| C22×C32×Dic5 | 2 |
| C2×#67137 | 2 |
| C5×#3757 | 2 |
| #10623774 | 2 |
| #10623772 | 2 |
| Dic5×C3⋊Dic3 | 2 |
| #91552 | 3 |
| C4×#638 | 5 |