Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 110 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. C2×C32×C5×C8 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. C3×#6705 | C2 | semidirect |
| 5. C3×C8×D15 | C2 | semidirect |
| 6. #91790 | C3 | direct (N × H) |
| 20. C2×C3×C5×C8 | D3 | semidirect |
| 21. C2×C3×C5×C8 | C2×C3 | semidirect |
| 22. #6710 | C2×C3 | semidirect |
| 23. #6705 | C2×C3 | semidirect |
| 24. C8×D15 | C2×C3 | semidirect |
| 35. C2×C32×C8 | D5 | semidirect |
| 64. C2×C5×C8 | C3×D3 | semidirect |
| 95. C2×C3×C8 | C3×D5 | semidirect |
| 96. C2×C3×C8 | D15 | semidirect |
| 100. C32×C5 | #131 | semidirect |
| 154. C2×C8 | C3×D15 | semidirect |
| 156. C3×C5 | #901 | semidirect |
| 157. C3×C5 | C3×#131 | semidirect |
| 174. C32 | #4047 | semidirect |
| 191. C5 | C3×#901 | semidirect |
| 198. C3 | C3×#4047 | semidirect |
| 199. C3 | #91790 | 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×#6710 | 2 |
| C3×#6705 | 2 |
| C3×C8×D15 | 2 |
| #91790 | 3 |
| C3×#4047 | 3 |
| C3×#901 | 5 |