Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 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×Q8 | C2 | semidirect |
| 3. C32×#689 | C2 | semidirect |
| 4. C32×#688 | C2 | semidirect |
| 5. C32×#681 | C2 | semidirect |
| 6. C3×#4088 | C3 | direct (N × H) |
| 17. C2×C3×C5×Q8 | C2×C3 | semidirect |
| 19. C3×#689 | C2×C3 | semidirect |
| 20. C3×#688 | C2×C3 | semidirect |
| 21. C3×#681 | C2×C3 | semidirect |
| 28. #4088 | C32 | direct (N × H) |
| 30. C2×C32×Q8 | D5 | semidirect |
| 47. C2×C5×Q8 | C2×C32 | semidirect |
| 49. #689 | C2×C32 | semidirect |
| 50. #688 | C2×C32 | semidirect |
| 51. #681 | C2×C32 | semidirect |
| 68. C2×C3×Q8 | C3×D5 | semidirect |
| 72. C32×C5 | #137 | semidirect |
| 111. C2×Q8 | C32×D5 | semidirect |
| 115. C3×C5 | C3×#137 | semidirect |
| 125. C32 | #4088 | direct (N × H) |
| 138. C5 | C32×#137 | semidirect |
| 145. C3 | C3×#4088 | 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×#709 | 2 |
| C32×#689 | 2 |
| C32×#688 | 2 |
| C32×#681 | 2 |
| C3×#4088 | 3 |
| C32×#137 | 5 |