Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. C3×D15⋊Q8 | C2 | semidirect |
| 3. C3×C8×D15 | C2 | semidirect |
| 4. C3×C5×#204 | C2 | semidirect |
| 5. C32×#677 | C2 | semidirect |
| 6. C3×#6656 | C2 | semidirect |
| 7. C3×#6655 | C2 | semidirect |
| 9. #91255 | C3 | direct (N × H) |
| 13. C3×C5×Dic6 | C22 | semidirect |
| 15. C32×Dic10 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 25. D15⋊Q8 | C2×C3 | semidirect |
| 27. C8×D15 | C2×C3 | semidirect |
| 28. C5×#204 | C2×C3 | semidirect |
| 32. C3×#677 | D3 | semidirect |
| 33. C3×#677 | C2×C3 | semidirect |
| 35. #6656 | C2×C3 | semidirect |
| 36. #6655 | C2×C3 | semidirect |
| 51. C3×#204 | D5 | semidirect |
| 59. C5×Dic6 | C22×C3 | semidirect |
| 68. C3×Dic10 | C2×D3 | semidirect |
| 69. C3×Dic10 | C22×C3 | semidirect |
| 74. C3×C5×C8 | C2×D3 | semidirect |
| 75. C3×C5×C8 | C22×C3 | semidirect |
| 76. C3⋊#168 | C22×C3 | semidirect |
| 81. C3×D15 | SD16 | semidirect |
| 89. #677 | C3×D3 | semidirect |
| 99. C3×Dic6 | C2×D5 | semidirect |
| 100. C32×C8 | C2×D5 | semidirect |
| 134. #204 | C3×D5 | semidirect |
| 136. C32×C5 | C2×SD16 | semidirect |
| 145. Dic10 | C2×C3×D3 | semidirect |
| 146. C5×C8 | C2×C3×D3 | semidirect |
| 161. D15 | C3×SD16 | semidirect |
| 186. Dic6 | C2×C3×D5 | semidirect |
| 189. C3×C8 | D3×D5 | semidirect |
| 190. C3×C8 | C2×C3×D5 | semidirect |
| 212. C3×C5 | D3×SD16 | semidirect |
| 213. C3×C5 | C2×C3×SD16 | semidirect |
| 237. C32 | D5×SD16 | semidirect |
| 248. C8 | C3×D3×D5 | semidirect |
| 259. C5 | C3×D3×SD16 | semidirect |
| 269. C3 | #91255 | direct (N × H) |
| 270. C3 | C3×D5×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6777 | 2 |
| C3×D15⋊Q8 | 2 |
| C3×C8×D15 | 2 |
| C3×C5×#204 | 2 |
| C32×#677 | 2 |
| C3×#6656 | 2 |
| C3×#6655 | 2 |
| C3×D5×SD16 | 3 |
| #91255 | 3 |
| C3×D3×SD16 | 5 |