Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 71 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. C3×C4⋊Dic15 | C2 | semidirect |
| 3. C3×#6712 | C2 | semidirect |
| 4. #10623831 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 18. C4⋊Dic15 | D3 | semidirect |
| 19. #6712 | D3 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #898 | semidirect |
| 200. C3×C5 | #898 | semidirect |
| 231. C32 | #4025 | semidirect |
| 251. C5 | #63848 | semidirect |
| 263. C3 | #91341 | semidirect |
| 264. C3 | #91342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3752 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×#6712 | 2 |
| #10623831 | 2 |
| #10623830 | 2 |
| #10623828 | 2 |
| #91342 | 3 |
| #91341 | 3 |
| #63848 | 5 |