Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. C3×#6712 | C2 | semidirect |
| 2. C3×C4×C5×Dic3 | C2 | semidirect |
| 4. C3×#6669 | C2 | semidirect |
| 5. C3×#6668 | C2 | semidirect |
| 9. #91363 | C3 | direct (N × H) |
| 19. #6712 | C2×C3 | semidirect |
| 20. C4×C5×Dic3 | C2×C3 | semidirect |
| 29. #6669 | C2×C3 | semidirect |
| 30. #6668 | C2×C3 | semidirect |
| 50. C3×C4×Dic3 | D5 | semidirect |
| 128. C4×Dic3 | C3×D5 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #879 | semidirect |
| 200. C3×C5 | C3×#126 | semidirect |
| 231. C32 | #4022 | semidirect |
| 251. C5 | C3×#879 | semidirect |
| 263. C3 | #91363 | direct (N × H) |
| 264. C3 | C3×#4022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6712 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C32×#685 | 2 |
| C3×#6669 | 2 |
| C3×#6668 | 2 |
| C3×#6665 | 2 |
| C3×#4022 | 3 |
| #91363 | 3 |
| C3×#879 | 5 |