Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 210 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. C2×C32×Dic10 | C2 | semidirect |
| 5. C32×C4⋊Dic5 | C2 | semidirect |
| 6. C32×#683 | C2 | semidirect |
| 7. C32×#683 | C2 | semidirect |
| 8. C3×#4024 | C3 | direct (N × H) |
| 20. C2×C3×Dic10 | C2×C3 | semidirect |
| 23. C3×C4⋊Dic5 | C2×C3 | semidirect |
| 24. C3×#683 | C2×C3 | semidirect |
| 25. C3×#683 | C2×C3 | semidirect |
| 28. C22×C32×C5 | Q8 | semidirect |
| 36. #4024 | C32 | direct (N × H) |
| 59. C2×Dic10 | C2×C32 | semidirect |
| 62. C4⋊Dic5 | C2×C32 | semidirect |
| 63. #683 | C2×C32 | semidirect |
| 64. #683 | C2×C32 | semidirect |
| 76. C22×C3×C5 | C3×Q8 | semidirect |
| 91. C32×C5 | C22⋊Q8 | semidirect |
| 103. C22×C32 | Dic10 | semidirect |
| 127. C22×C5 | C32×Q8 | semidirect |
| 146. C3×C5 | C3×C22⋊Q8 | semidirect |
| 149. C22×C3 | C3×Dic10 | semidirect |
| 161. C32 | #4024 | direct (N × H) |
| 175. C5 | C32×C22⋊Q8 | semidirect |
| 178. C22 | C32×Dic10 | semidirect |
| 186. C3 | C3×#4024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Dic5 | 2 |
| C2×C32×Dic10 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×C4⋊Dic5 | 2 |
| C32×#683 | 2 |
| C3×#4024 | 3 |
| C32×C22⋊Q8 | 5 |