Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 174 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. C2×C32×C5×D4 | C2 | semidirect |
| 2. C32×#709 | C2 | semidirect |
| 3. C32×#687 | C2 | semidirect |
| 4. C32×#686 | C2 | semidirect |
| 5. C32×#681 | C2 | semidirect |
| 6. C3×#4078 | C3 | direct (N × H) |
| 12. C32×D20 | C22 | semidirect |
| 14. C32×Dic10 | C22 | semidirect |
| 15. C32×#168 | C22 | semidirect |
| 17. C2×C3×C5×D4 | C2×C3 | semidirect |
| 18. C3×#709 | C2×C3 | semidirect |
| 19. C3×#687 | C2×C3 | semidirect |
| 20. C3×#686 | C2×C3 | semidirect |
| 21. C3×#681 | C2×C3 | semidirect |
| 29. #4078 | C32 | direct (N × H) |
| 31. C2×C32×D4 | D5 | semidirect |
| 40. C3×D20 | C22×C3 | semidirect |
| 42. C3×Dic10 | C22×C3 | semidirect |
| 43. C3×#168 | C22×C3 | semidirect |
| 49. C2×C5×D4 | C2×C32 | semidirect |
| 50. #709 | C2×C32 | semidirect |
| 51. #687 | C2×C32 | semidirect |
| 52. #686 | C2×C32 | semidirect |
| 53. #681 | C2×C32 | semidirect |
| 71. C2×C3×D4 | C3×D5 | semidirect |
| 75. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 81. D20 | C22×C32 | semidirect |
| 83. Dic10 | C22×C32 | semidirect |
| 84. #168 | C22×C32 | semidirect |
| 118. C2×D4 | C32×D5 | semidirect |
| 122. C3×C5 | C3×AGL(1,ℤ/8) | semidirect |
| 134. C32 | #4078 | direct (N × H) |
| 148. C5 | C32×AGL(1,ℤ/8) | semidirect |
| 156. C3 | C3×#4078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C32×#709 | 2 |
| C32×#687 | 2 |
| C32×#686 | 2 |
| C32×#681 | 2 |
| C3×#4078 | 3 |
| C32×AGL(1,ℤ/8) | 5 |