Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 96 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×#6758 | C2 | semidirect |
| 3. C32×#700 | C2 | semidirect |
| 4. C3×#6739 | C2 | semidirect |
| 5. C3×#6738 | C2 | semidirect |
| 7. #91915 | C3 | direct (N × H) |
| 15. C3×C3⋊#170 | C22 | semidirect |
| 16. C32×#170 | C22 | semidirect |
| 20. #6758 | C2×C3 | semidirect |
| 24. C3×#700 | D3 | semidirect |
| 25. C3×#700 | C2×C3 | semidirect |
| 27. #6739 | C2×C3 | semidirect |
| 28. #6738 | C2×C3 | semidirect |
| 58. C3⋊#170 | C22×C3 | semidirect |
| 61. C3×#170 | C2×D3 | semidirect |
| 62. C3×#170 | C22×C3 | semidirect |
| 66. C3×D15 | M16 | semidirect |
| 72. #700 | C3×D3 | semidirect |
| 113. C32×C5 | C2×M16 | semidirect |
| 122. #170 | C2×C3×D3 | semidirect |
| 136. D15 | C3×M16 | semidirect |
| 180. C3×C5 | D3×M16 | semidirect |
| 181. C3×C5 | C2×C3×M16 | semidirect |
| 205. C32 | D5⋊M16 | semidirect |
| 225. C5 | C3×D3×M16 | semidirect |
| 235. C3 | #91915 | direct (N × H) |
| 236. C3 | C3×D5⋊M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D3×D5 | 2 |
| C3×#6758 | 2 |
| C32×#700 | 2 |
| C3×#6739 | 2 |
| C3×#6738 | 2 |
| C3×D5⋊M16 | 3 |
| #91915 | 3 |
| C3×D3×M16 | 5 |