Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 62 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. C3×#6821 | C2 | semidirect |
| 2. #10624200 | C2 | semidirect |
| 3. #10623912 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. #10623803 | C2 | semidirect |
| 6. #10623798 | C2 | semidirect |
| 7. C3⋊C8×D15 | C2 | semidirect |
| 22. #6821 | D3 | semidirect |
| 33. C5×#215 | D3 | semidirect |
| 48. C3×#215 | D5 | semidirect |
| 126. #215 | D15 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 206. C3×C5 | #916 | semidirect |
| 207. C3×C5 | #950 | semidirect |
| 229. C32 | #4062 | semidirect |
| 250. C5 | #63947 | semidirect |
| 259. C3 | #91514 | semidirect |
| 260. C3 | #91805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6821 | 2 |
| #10624200 | 2 |
| #10623912 | 2 |
| C3×C5×#215 | 2 |
| #10623803 | 2 |
| #10623798 | 2 |
| C3⋊C8×D15 | 2 |
| #91805 | 3 |
| #91514 | 3 |
| #63947 | 5 |