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×C4⋊Dic15 | C2 | semidirect |
| 2. C3×C5×Dic3⋊C4 | C2 | semidirect |
| 4. C3×#6669 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 9. #91362 | C3 | direct (N × H) |
| 19. C4⋊Dic15 | C2×C3 | semidirect |
| 20. C5×Dic3⋊C4 | C2×C3 | semidirect |
| 29. #6669 | C2×C3 | semidirect |
| 32. Dic3×Dic5 | C2×C3 | semidirect |
| 49. C3×Dic3⋊C4 | D5 | semidirect |
| 127. Dic3⋊C4 | C3×D5 | semidirect |
| 129. C32×C5 | #126 | semidirect |
| 199. C3×C5 | #879 | semidirect |
| 200. C3×C5 | C3×#126 | semidirect |
| 231. C32 | #4044 | semidirect |
| 251. C5 | C3×#879 | semidirect |
| 263. C3 | #91362 | direct (N × H) |
| 264. C3 | C3×#4044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊Dic15 | 2 |
| C3×C5×Dic3⋊C4 | 2 |
| C32×#685 | 2 |
| C3×#6669 | 2 |
| C3×#6665 | 2 |
| C3×Dic3×Dic5 | 2 |
| C3×#4044 | 3 |
| #91362 | 3 |
| C3×#879 | 5 |