Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 292 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. D12×D15 | C2 | semidirect |
| 2. #10624200 | C2 | semidirect |
| 3. #10623900 | C2 | semidirect |
| 4. C3×#6705 | C2 | semidirect |
| 5. C3×C5×D24 | C2 | semidirect |
| 6. #10623805 | C2 | semidirect |
| 7. #10623800 | C2 | semidirect |
| 12. #67180 | C22 | semidirect |
| 15. C3×C5×D12 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 32. #6705 | D3 | semidirect |
| 33. C5×D24 | D3 | semidirect |
| 49. C3×D24 | D5 | semidirect |
| 68. C5×D12 | C2×D3 | semidirect |
| 74. C3×C5×C8 | C2×D3 | semidirect |
| 75. C3×C5×C8 | C2×D3 | semidirect |
| 76. C3⋊#168 | C2×D3 | semidirect |
| 96. C3×D12 | C2×D5 | semidirect |
| 101. C32×C8 | C2×D5 | semidirect |
| 131. D24 | D15 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 147. C5×C8 | D32 | semidirect |
| 184. D12 | C2×D15 | semidirect |
| 192. C3×C8 | D3×D5 | semidirect |
| 193. C3×C8 | C2×D15 | semidirect |
| 216. C3×C5 | #908 | semidirect |
| 217. C3×C5 | #911 | semidirect |
| 242. C32 | #4057 | semidirect |
| 253. C8 | D3×D15 | semidirect |
| 266. C5 | #63795 | semidirect |
| 276. C3 | #91250 | semidirect |
| 277. C3 | #91800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D12×D15 | 2 |
| #10624200 | 2 |
| #10623900 | 2 |
| C3×#6705 | 2 |
| C3×C5×D24 | 2 |
| #10623805 | 2 |
| #10623800 | 2 |
| #91800 | 3 |
| #91250 | 3 |
| #63795 | 5 |