Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 2. C32×#704 | C2 | semidirect |
| 3. C2×C32×#170 | C2 | semidirect |
| 4. C32×#700 | C2 | semidirect |
| 5. C32×D5⋊C8 | C2 | semidirect |
| 6. C3×#4131 | C3 | direct (N × H) |
| 17. C3×#704 | C2×C3 | semidirect |
| 18. C2×C3×#170 | C2×C3 | semidirect |
| 19. C3×#700 | C2×C3 | semidirect |
| 20. C3×D5⋊C8 | C2×C3 | semidirect |
| 26. #4131 | C32 | direct (N × H) |
| 45. #704 | C2×C32 | semidirect |
| 46. C2×#170 | C2×C32 | semidirect |
| 47. #700 | C2×C32 | semidirect |
| 48. D5⋊C8 | C2×C32 | semidirect |
| 67. C32×C5 | #131 | semidirect |
| 106. C3×C5 | C3×#131 | semidirect |
| 115. C32 | #4131 | direct (N × H) |
| 127. C5 | C32×#131 | semidirect |
| 133. C3 | C3×#4131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#711 | 2 |
| C32×#704 | 2 |
| C2×C32×#170 | 2 |
| C32×#700 | 2 |
| C32×D5⋊C8 | 2 |
| C3×#4131 | 3 |
| C32×#131 | 5 |