Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
422 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 4. #10623831 | C2 | direct (N × H) |
| 11. C2×C3×Dic15 | C4 | semidirect |
| 30. C3×Dic15 | C2×C4 | semidirect |
| 40. C2×Dic15 | Dic3 | semidirect |
| 55. C2×C32×C5 | C4⋊C4 | semidirect |
| 83. Dic15 | C2×Dic3 | semidirect |
| 98. C32×C5 | C2×C4⋊C4 | semidirect |
| 118. C2×C3×C5 | Dic3⋊C4 | semidirect |
| 119. C2×C3×C5 | C4⋊Dic3 | semidirect |
| 150. C2×C32 | #683 | semidirect |
| 159. C3×C5 | C2×Dic3⋊C4 | semidirect |
| 160. C3×C5 | C2×C4⋊Dic3 | semidirect |
| 180. C2×C5 | Dic3⋊Dic3 | semidirect |
| 184. C32 | C2×#683 | semidirect |
| 196. C2×C3 | #6668 | semidirect |
| 197. C2×C3 | #6669 | semidirect |
| 204. C5 | C2×Dic3⋊Dic3 | semidirect |
| 213. C3 | C2×#6668 | semidirect |
| 214. C3 | C2×#6669 | semidirect |
| 215. C2 | #10623831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C22×C3×Dic15 | 2 |
| #10623831 | 2 |
| C2×#6669 | 3 |
| C2×#6668 | 3 |
| C2×Dic3⋊Dic3 | 5 |