Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 4. C3×C4⋊Dic15 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. C3×#6712 | C2 | semidirect |
| 7. C3×C4×Dic15 | C2 | semidirect |
| 8. #91768 | C3 | direct (N × H) |
| 23. C4⋊Dic15 | C2×C3 | semidirect |
| 24. #6712 | C2×C3 | semidirect |
| 25. #6712 | C2×C3 | semidirect |
| 26. C4×Dic15 | C2×C3 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #879 | semidirect |
| 200. C3×C5 | C3×#126 | semidirect |
| 231. C32 | #4025 | semidirect |
| 251. C5 | C3×#879 | semidirect |
| 263. C3 | C3×#4025 | semidirect |
| 264. C3 | #91768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C22⋊C4 | 2 |
| C3×#6719 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×#6712 | 2 |
| C3×C4×Dic15 | 2 |
| #91768 | 3 |
| C3×#4025 | 3 |
| C3×#879 | 5 |