Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
298 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 6. #91777 | C3 | direct (N × H) |
| 28. C32×C4×C5 | Q8 | semidirect |
| 31. C3×Dic15 | Q8 | semidirect |
| 75. C3×C4×C5 | Dic6 | semidirect |
| 76. C3×C4×C5 | C3×Q8 | semidirect |
| 79. Dic15 | C3×Q8 | semidirect |
| 94. C32×C5 | C4⋊Q8 | semidirect |
| 103. C32×C4 | Dic10 | semidirect |
| 133. C4×C5 | C3×Dic6 | semidirect |
| 146. C3×C5 | #888 | semidirect |
| 147. C3×C5 | C3×C4⋊Q8 | semidirect |
| 158. C3×C4 | C3×Dic10 | semidirect |
| 159. C3×C4 | Dic30 | semidirect |
| 166. C32 | #4034 | semidirect |
| 182. C5 | C3×#888 | semidirect |
| 188. C4 | C3×Dic30 | semidirect |
| 190. C3 | C3×#4034 | semidirect |
| 191. C3 | #91777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic30 | 2 |
| C32×C5×C4⋊C4 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×#6712 | 2 |
| C3×C4×Dic15 | 2 |
| #91777 | 3 |
| C3×#4034 | 3 |
| C3×#888 | 5 |