Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
318 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 7. #91331 | C3 | direct (N × H) |
| 13. C32×Dic10 | C4 | semidirect |
| 29. C3×Dic15 | Q8 | semidirect |
| 51. C3×Dic10 | Dic3 | semidirect |
| 52. C3×Dic10 | C3×C4 | semidirect |
| 77. Dic15 | C3×Q8 | semidirect |
| 95. C32×C5 | C4×Q8 | semidirect |
| 101. Dic10 | C3×Dic3 | semidirect |
| 148. C3×C5 | Q8×Dic3 | semidirect |
| 149. C3×C5 | C3×C4×Q8 | semidirect |
| 168. C32 | #4033 | semidirect |
| 184. C5 | C3×Q8×Dic3 | semidirect |
| 192. C3 | #91331 | direct (N × H) |
| 193. C3 | C3×#4033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic10 | 2 |
| C3×C4×Dic15 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C3×#6668 | 2 |
| C3×Dic3×Dic5 | 2 |
| C3×#4033 | 3 |
| #91331 | 3 |
| C3×Q8×Dic3 | 5 |