Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 372 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. C32×C5×#41 | C2 | semidirect |
| 2. C32×#709 | C2 | semidirect |
| 3. C32×#689 | C2 | semidirect |
| 4. C32×#688 | C2 | semidirect |
| 5. C32×#687 | C2 | semidirect |
| 6. C32×#686 | C2 | semidirect |
| 7. C2×C32×#168 | C2 | semidirect |
| 8. C3×#4096 | C3 | direct (N × H) |
| 21. C3×C5×#41 | C2×C3 | semidirect |
| 22. C3×#709 | C2×C3 | semidirect |
| 23. C3×#689 | C2×C3 | semidirect |
| 24. C3×#688 | C2×C3 | semidirect |
| 25. C3×#687 | C2×C3 | semidirect |
| 26. C3×#686 | C2×C3 | semidirect |
| 27. C2×C3×#168 | C2×C3 | semidirect |
| 35. #4096 | C32 | direct (N × H) |
| 37. C32×#41 | D5 | semidirect |
| 59. C5×#41 | C2×C32 | semidirect |
| 60. #709 | C2×C32 | semidirect |
| 61. #689 | C2×C32 | semidirect |
| 62. #688 | C2×C32 | semidirect |
| 63. #687 | C2×C32 | semidirect |
| 64. #686 | C2×C32 | semidirect |
| 65. C2×#168 | C2×C32 | semidirect |
| 85. C3×#41 | C3×D5 | semidirect |
| 91. C32×C5 | #135 | semidirect |
| 138. #41 | C32×D5 | semidirect |
| 144. C3×C5 | C3×#135 | semidirect |
| 156. C32 | #4096 | direct (N × H) |
| 172. C5 | C32×#135 | semidirect |
| 180. C3 | C3×#4096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×#41 | 2 |
| C32×#709 | 2 |
| C32×#689 | 2 |
| C32×#688 | 2 |
| C32×#687 | 2 |
| C32×#686 | 2 |
| C2×C32×#168 | 2 |
| C3×#4096 | 3 |
| C32×#135 | 5 |