Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. C3×#6712 | C2 | semidirect |
| 4. C3×C4×Dic15 | C2 | semidirect |
| 5. #10623831 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 17. #67155 | C4 | semidirect |
| 21. #6712 | D3 | semidirect |
| 22. C4×Dic15 | D3 | semidirect |
| 133. C32×C5 | #117 | semidirect |
| 206. C3×C5 | #872 | semidirect |
| 207. C3×C5 | #892 | semidirect |
| 238. C32 | #4023 | semidirect |
| 259. C5 | #63836 | semidirect |
| 271. C3 | #91398 | semidirect |
| 272. C3 | #91400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67155 | 2 |
| C5×#3752 | 2 |
| C3×#6712 | 2 |
| C3×C4×Dic15 | 2 |
| #10623831 | 2 |
| #10623830 | 2 |
| #10623828 | 2 |
| #91400 | 3 |
| #91398 | 3 |
| #63836 | 5 |