Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 104 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×#67180 | C2 | semidirect |
| 3. C5×#3748 | C2 | semidirect |
| 4. #10623767 | C2 | semidirect |
| 5. #10623762 | C2 | semidirect |
| 33. #3748 | D5 | semidirect |
| 72. C32×C5 | #137 | semidirect |
| 115. C3×C5 | #951 | semidirect |
| 125. C32 | #4055 | semidirect |
| 138. C5 | #64160 | semidirect |
| 145. C3 | #91313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C32×#709 | 2 |
| C5×#3748 | 2 |
| #10623767 | 2 |
| #10623762 | 2 |
| #91313 | 3 |
| #64160 | 5 |