Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
366 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 110 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×C3×Dic15 | C2 | semidirect |
| 3. C3×#6719 | C2 | semidirect |
| 4. C3×#6719 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. #91824 | C3 | direct (N × H) |
| 19. C22×Dic15 | C2×C3 | semidirect |
| 21. #6719 | C2×C3 | semidirect |
| 22. #6719 | C2×C3 | semidirect |
| 23. #6712 | C2×C3 | semidirect |
| 110. C32×C5 | #123 | semidirect |
| 175. C3×C5 | #935 | semidirect |
| 176. C3×C5 | C3×#123 | semidirect |
| 203. C32 | #4081 | semidirect |
| 223. C5 | C3×#935 | semidirect |
| 233. C3 | C3×#4081 | semidirect |
| 234. C3 | #91824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C22×C3×Dic15 | 2 |
| C3×#6719 | 2 |
| C3×#6712 | 2 |
| #91824 | 3 |
| C3×#4081 | 3 |
| C3×#935 | 5 |