Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 62 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. #10624205 | C2 | semidirect |
| 2. C8×C3⋊D15 | C2 | semidirect |
| 3. C3×D120 | C2 | semidirect |
| 4. C3×C5×D24 | C2 | semidirect |
| 5. #10623798 | C2 | semidirect |
| 10. C3×D60 | C22 | semidirect |
| 11. C3×C5×D12 | C22 | semidirect |
| 13. C32×C5×C8 | C22 | semidirect |
| 14. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. D120 | D3 | semidirect |
| 24. C5×D24 | D3 | semidirect |
| 37. C3×D24 | D5 | semidirect |
| 43. D60 | C2×D3 | semidirect |
| 47. C5×D12 | C2×D3 | semidirect |
| 51. C3×C5×C8 | C2×D3 | semidirect |
| 52. C3×C5×C8 | C2×D3 | semidirect |
| 59. C3⋊D15 | D8 | semidirect |
| 70. C3×D12 | C2×D5 | semidirect |
| 72. C32×C8 | C2×D5 | semidirect |
| 96. D24 | D15 | semidirect |
| 100. C32×C5 | C2×D8 | semidirect |
| 106. C5×C8 | D32 | semidirect |
| 132. D12 | C2×D15 | semidirect |
| 137. C3×C8 | D3×D5 | semidirect |
| 138. C3×C8 | C2×D15 | semidirect |
| 158. C3×C5 | D3×D8 | semidirect |
| 159. C3×C5 | D3×D8 | semidirect |
| 179. C32 | D5×D8 | semidirect |
| 186. C8 | D3×D15 | semidirect |
| 197. C5 | #63797 | semidirect |
| 205. C3 | #91256 | semidirect |
| 206. C3 | D8×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624205 | 2 |
| C8×C3⋊D15 | 2 |
| C3×D120 | 2 |
| C3×C5×D24 | 2 |
| #10623798 | 2 |
| D8×D15 | 3 |
| #91256 | 3 |
| #63797 | 5 |