Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 258 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×Q8×D15 | C2 | semidirect |
| 3. #10623912 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. #10623808 | C2 | semidirect |
| 6. #10623802 | C2 | semidirect |
| 7. #10623795 | C2 | semidirect |
| 22. Q8×D15 | D3 | semidirect |
| 33. C5×#215 | D3 | semidirect |
| 48. C3×#215 | D5 | semidirect |
| 127. #215 | D15 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #915 | semidirect |
| 203. C3×C5 | #942 | semidirect |
| 224. C32 | #4061 | semidirect |
| 243. C5 | #63946 | semidirect |
| 252. C3 | #91513 | semidirect |
| 253. C3 | #91804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D15 | 2 |
| #10624200 | 2 |
| #10623912 | 2 |
| C3×C5×#215 | 2 |
| #10623808 | 2 |
| #10623802 | 2 |
| #10623795 | 2 |
| #91804 | 3 |
| #91513 | 3 |
| #63946 | 5 |