Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
|---|---|---|
| 5. C3×#4090 | C3 | direct (N × H) |
| 21. C32×Dic5 | Q8 | semidirect |
| 22. #4090 | C32 | direct (N × H) |
| 50. C3×Dic5 | C3×Q8 | semidirect |
| 55. C32×C5 | C4⋊Q8 | semidirect |
| 80. Dic5 | C32×Q8 | semidirect |
| 87. C3×C5 | C3×C4⋊Q8 | semidirect |
| 95. C32 | #4090 | direct (N × H) |
| 104. C5 | C32×C4⋊Q8 | semidirect |
| 110. C3 | C3×#4090 | 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 |
| C2×C32×Dic10 | 2 |
| C32×#683 | 2 |
| C32×C4×Dic5 | 2 |
| C3×#4090 | 3 |
| C32×C4⋊Q8 | 5 |