Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 1. C3×D3×D20 | C2 | semidirect |
| 2. C3×#6765 | C2 | semidirect |
| 3. C3×#6706 | C2 | semidirect |
| 4. C3×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 5. C32×D40 | C2 | semidirect |
| 6. C3×#6657 | C2 | semidirect |
| 7. C3×#6653 | C2 | semidirect |
| 9. #91254 | C3 | direct (N × H) |
| 12. C3×Dic30 | C22 | semidirect |
| 15. C32×D20 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 24. D3×D20 | C2×C3 | semidirect |
| 25. #6765 | C2×C3 | semidirect |
| 27. #6706 | C2×C3 | semidirect |
| 28. C5×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 31. C3×D40 | D3 | semidirect |
| 32. C3×D40 | C2×C3 | semidirect |
| 35. #6657 | C2×C3 | semidirect |
| 36. #6653 | C2×C3 | semidirect |
| 52. C3×ΓL(1,𝔽25) | D5 | semidirect |
| 57. Dic30 | C22×C3 | semidirect |
| 65. C3×D20 | C2×D3 | semidirect |
| 67. C3×D20 | C22×C3 | semidirect |
| 75. C3×C5×C8 | C2×D3 | semidirect |
| 76. C3×C5×C8 | C22×C3 | semidirect |
| 77. C5×C3⋊C8 | C22×C3 | semidirect |
| 89. D40 | C3×D3 | semidirect |
| 101. C32×C8 | C2×D5 | semidirect |
| 102. C3×C3⋊C8 | C2×D5 | semidirect |
| 136. ΓL(1,𝔽25) | C3×D5 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 144. D20 | C2×C3×D3 | semidirect |
| 148. C5×C8 | C2×C3×D3 | semidirect |
| 193. C3×C8 | D3×D5 | semidirect |
| 194. C3×C8 | C2×C3×D5 | semidirect |
| 195. C3⋊C8 | C2×C3×D5 | semidirect |
| 217. C3×C5 | #911 | semidirect |
| 218. C3×C5 | C3×AGL(1,ℤ/8) | semidirect |
| 243. C32 | #4054 | semidirect |
| 254. C8 | C3×D3×D5 | semidirect |
| 268. C5 | C3×#911 | semidirect |
| 278. C3 | #91254 | direct (N × H) |
| 279. C3 | C3×#4054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×D20 | 2 |
| C3×#6765 | 2 |
| C3×#6706 | 2 |
| C3×C5×ΓL(1,𝔽25) | 2 |
| C32×D40 | 2 |
| C3×#6657 | 2 |
| C3×#6653 | 2 |
| C3×#4054 | 3 |
| #91254 | 3 |
| C3×#911 | 5 |