Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10624093 | C2 | semidirect |
| 3. C3×D5⋊(C3⋊C8) | C2 | semidirect |
| 4. #10623976 | C2 | semidirect |
| 5. #10623974 | C2 | semidirect |
| 24. D5⋊(C3⋊C8) | D3 | semidirect |
| 99. C32×C5 | #131 | semidirect |
| 154. C3×C5 | #901 | semidirect |
| 155. C3×C5 | #948 | semidirect |
| 172. C32 | #4133 | semidirect |
| 189. C5 | #63814 | semidirect |
| 196. C3 | #91914 | semidirect |
| 197. C3 | #91992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6773 | 2 |
| #10624093 | 2 |
| C3×D5⋊(C3⋊C8) | 2 |
| #10623976 | 2 |
| #10623974 | 2 |
| #91992 | 3 |
| #91914 | 3 |
| #63814 | 5 |