Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10623911 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. #10623804 | C2 | semidirect |
| 6. #10623802 | C2 | semidirect |
| 7. C3⋊C8×D15 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 16. C3×Dic30 | C22 | semidirect |
| 19. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 22. Q8×D15 | D3 | semidirect |
| 33. C5×#215 | D3 | semidirect |
| 49. C3×#215 | D5 | semidirect |
| 56. C3×C5×Q8 | C2×D3 | semidirect |
| 57. C3×C5×Q8 | C2×D3 | semidirect |
| 66. Dic30 | C2×D3 | semidirect |
| 77. C5×C3⋊C8 | C2×D3 | semidirect |
| 82. C3×D15 | SD16 | semidirect |
| 92. C32×Q8 | C2×D5 | semidirect |
| 101. C3×C3⋊C8 | C2×D5 | semidirect |
| 131. #215 | D15 | direct (N × H) |
| 136. C32×C5 | C2×SD16 | semidirect |
| 138. C5×Q8 | D32 | semidirect |
| 164. D15 | #215 | direct (N × H) |
| 172. C3×Q8 | D3×D5 | semidirect |
| 173. C3×Q8 | C2×D15 | semidirect |
| 191. C3⋊C8 | C2×D15 | semidirect |
| 212. C3×C5 | D3×SD16 | semidirect |
| 213. C3×C5 | C2×#215 | semidirect |
| 237. C32 | D5×SD16 | semidirect |
| 241. Q8 | D3×D15 | semidirect |
| 259. C5 | D3×#215 | semidirect |
| 269. C3 | D5×#215 | semidirect |
| 270. C3 | SD16×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D15 | 2 |
| D12×D15 | 2 |
| #10623911 | 2 |
| C3×C5×#215 | 2 |
| #10623804 | 2 |
| #10623802 | 2 |
| C3⋊C8×D15 | 2 |
| SD16×D15 | 3 |
| D5×#215 | 3 |
| D3×#215 | 5 |