Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 59 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×#6821 | C2 | semidirect |
| 2. #10624226 | C2 | semidirect |
| 3. C5×#3755 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. #10623822 | C2 | semidirect |
| 6. #10623821 | C2 | semidirect |
| 7. #10623819 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 15. C3×D60 | C22 | semidirect |
| 19. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 22. #6821 | D3 | semidirect |
| 26. #6717 | D3 | semidirect |
| 48. #3755 | D5 | semidirect |
| 56. C3×C5×Q8 | C2×D3 | semidirect |
| 57. C3×C5×Q8 | C2×D3 | semidirect |
| 60. D60 | C2×D3 | semidirect |
| 73. C3⋊#168 | C2×D3 | semidirect |
| 93. C32×Q8 | C2×D5 | semidirect |
| 101. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 139. C5×Q8 | D32 | semidirect |
| 173. C3×Q8 | D3×D5 | semidirect |
| 174. C3×Q8 | D3×D5 | semidirect |
| 216. C3×C5 | #914 | semidirect |
| 217. C3×C5 | #949 | semidirect |
| 242. C32 | #4060 | semidirect |
| 244. Q8 | (C3⋊D3)⋊D5 | semidirect |
| 266. C5 | #63939 | semidirect |
| 276. C3 | #91502 | semidirect |
| 277. C3 | #91506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6821 | 2 |
| #10624226 | 2 |
| C5×#3755 | 2 |
| C3×#6717 | 2 |
| #10623822 | 2 |
| #10623821 | 2 |
| #10623819 | 2 |
| #91506 | 3 |
| #91502 | 3 |
| #63939 | 5 |