Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 292 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. C3×Q8×D15 | C2 | semidirect |
| 3. C5×#3755 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. #10623825 | C2 | semidirect |
| 6. #10623824 | C2 | semidirect |
| 7. #10623817 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 17. C3×Dic30 | C22 | semidirect |
| 19. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 22. Q8×D15 | D3 | semidirect |
| 26. #6717 | D3 | semidirect |
| 48. #3755 | D5 | semidirect |
| 56. C3×C5×Q8 | C2×D3 | semidirect |
| 57. C3×C5×Q8 | C2×D3 | semidirect |
| 62. Dic30 | C2×D3 | semidirect |
| 73. C3⋊#168 | C2×D3 | semidirect |
| 83. C3×D15 | SD16 | semidirect |
| 92. C32×Q8 | C2×D5 | semidirect |
| 100. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 136. C32×C5 | C2×SD16 | semidirect |
| 138. C5×Q8 | D32 | semidirect |
| 161. D15 | #215 | semidirect |
| 172. C3×Q8 | D3×D5 | semidirect |
| 173. C3×Q8 | D3×D5 | semidirect |
| 212. C3×C5 | D3×SD16 | semidirect |
| 213. C3×C5 | C2×#215 | semidirect |
| 237. C32 | D5×SD16 | semidirect |
| 241. Q8 | (C3⋊D3)⋊D5 | semidirect |
| 259. C5 | D3×#215 | semidirect |
| 269. C3 | D5×#215 | semidirect |
| 270. C3 | #91505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D15 | 2 |
| #10624226 | 2 |
| C5×#3755 | 2 |
| C3×#6717 | 2 |
| #10623825 | 2 |
| #10623824 | 2 |
| #10623817 | 2 |
| #91505 | 3 |
| D5×#215 | 3 |
| D3×#215 | 5 |