Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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. #10624226 | C2 | semidirect |
| 2. C5×#3745 | C2 | semidirect |
| 3. C3×D120 | C2 | semidirect |
| 4. C3×C8×D15 | C2 | semidirect |
| 5. #10623821 | C2 | semidirect |
| 9. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 10. C3×D60 | C22 | semidirect |
| 13. C32×C5×C8 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 18. D120 | D3 | semidirect |
| 19. C8×D15 | D3 | semidirect |
| 35. #3745 | D5 | semidirect |
| 41. D60 | C2×D3 | semidirect |
| 51. C3×C5×C8 | C2×D3 | semidirect |
| 52. C3×C5×C8 | C2×D3 | semidirect |
| 53. C3⋊#168 | C2×D3 | semidirect |
| 60. C3×D15 | D8 | semidirect |
| 67. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 71. C32×C8 | C2×D5 | semidirect |
| 98. C32×C5 | C2×D8 | semidirect |
| 104. C5×C8 | D32 | semidirect |
| 117. D15 | D24 | semidirect |
| 136. C3×C8 | D3×D5 | semidirect |
| 137. C3×C8 | D3×D5 | semidirect |
| 155. C3×C5 | C2×D24 | semidirect |
| 156. C3×C5 | D3×D8 | semidirect |
| 175. C32 | D5×D8 | semidirect |
| 182. C8 | (C3⋊D3)⋊D5 | semidirect |
| 193. C5 | D3×D24 | semidirect |
| 201. C3 | D5×D24 | semidirect |
| 202. C3 | #91256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624226 | 2 |
| C5×#3745 | 2 |
| C3×D120 | 2 |
| C3×C8×D15 | 2 |
| #10623821 | 2 |
| #91256 | 3 |
| D5×D24 | 3 |
| D3×D24 | 5 |