Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 116 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×#67141 | C2 | semidirect |
| 3. #10623908 | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C32×C4×Dic5 | C2 | semidirect |
| 6. #10623772 | C2 | semidirect |
| 7. #10623771 | C2 | semidirect |
| 23. C3×C4×Dic5 | D3 | semidirect |
| 45. #3752 | D5 | semidirect |
| 67. C4×Dic5 | C3⋊D3 | semidirect |
| 96. C32×C5 | #124 | semidirect |
| 157. C3×C5 | #875 | semidirect |
| 175. C32 | #4031 | semidirect |
| 190. C5 | #64084 | semidirect |
| 203. C3 | #91350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67141 | 2 |
| C2×#67140 | 2 |
| #10623908 | 2 |
| C5×#3752 | 2 |
| C32×C4×Dic5 | 2 |
| #10623772 | 2 |
| #10623771 | 2 |
| #91350 | 3 |
| #64084 | 5 |