Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
876 conjugacy classes of subgroups; only the 510 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 510 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×Q8 | C2 | semidirect |
| 2. C32×#713 | C2 | semidirect |
| 3. C32×Q8×D5 | C2 | semidirect |
| 4. C32×#709 | C2 | semidirect |
| 5. C3×#4147 | C3 | direct (N × H) |
| 13. C2×C3×C5×Q8 | C2×C3 | semidirect |
| 14. C3×#713 | C2×C3 | semidirect |
| 15. C3×Q8×D5 | C2×C3 | semidirect |
| 16. C3×#709 | C2×C3 | semidirect |
| 21. #4147 | C32 | direct (N × H) |
| 25. C2×C32×Q8 | D5 | semidirect |
| 36. C2×C5×Q8 | C2×C32 | semidirect |
| 37. #713 | C2×C32 | semidirect |
| 38. Q8×D5 | C2×C32 | semidirect |
| 39. #709 | C2×C32 | semidirect |
| 53. C2×C3×Q8 | C3×D5 | semidirect |
| 54. C32×C5 | 2−1+4 | semidirect |
| 85. C2×Q8 | C32×D5 | semidirect |
| 86. C3×C5 | C3×2−1+4 | semidirect |
| 94. C32 | #4147 | direct (N × H) |
| 104. C5 | C32×2−1+4 | semidirect |
| 109. C3 | C3×#4147 | 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×Q8 | 2 |
| C32×#713 | 2 |
| C32×Q8×D5 | 2 |
| C32×#709 | 2 |
| C3×#4147 | 3 |
| C32×2−1+4 | 5 |