Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 1. C3×#6817 | C2 | semidirect |
| 2. C2×C32×C5×C8 | C2 | semidirect |
| 3. C3×Dic60 | C2 | semidirect |
| 4. C3×D120 | C2 | semidirect |
| 5. C3×#6706 | C2 | semidirect |
| 6. #91793 | C3 | direct (N × H) |
| 16. #6817 | C2×C3 | semidirect |
| 19. C2×C3×C5×C8 | D3 | semidirect |
| 20. C2×C3×C5×C8 | C2×C3 | semidirect |
| 21. Dic60 | C2×C3 | semidirect |
| 22. D120 | C2×C3 | semidirect |
| 23. #6706 | C2×C3 | semidirect |
| 34. C2×C32×C8 | D5 | semidirect |
| 61. C2×C5×C8 | C3×D3 | semidirect |
| 91. C2×C3×C8 | C3×D5 | semidirect |
| 92. C2×C3×C8 | D15 | semidirect |
| 96. C32×C5 | #135 | semidirect |
| 147. C2×C8 | C3×D15 | semidirect |
| 149. C3×C5 | #904 | semidirect |
| 150. C3×C5 | C3×#135 | semidirect |
| 167. C32 | #4050 | semidirect |
| 183. C5 | C3×#904 | semidirect |
| 190. C3 | C3×#4050 | semidirect |
| 191. C3 | #91793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| C2×C32×C5×C8 | 2 |
| C3×Dic60 | 2 |
| C3×D120 | 2 |
| C3×#6706 | 2 |
| #91793 | 3 |
| C3×#4050 | 3 |
| C3×#904 | 5 |