Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 60 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. Q8×C3⋊D15 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. #10623808 | C2 | semidirect |
| 6. #10623805 | C2 | semidirect |
| 7. #10623797 | C2 | semidirect |
| 28. #6718 | D3 | semidirect |
| 32. C5×#215 | D3 | semidirect |
| 48. C3×#215 | D5 | semidirect |
| 130. #215 | D15 | semidirect |
| 136. C32×C5 | #137 | semidirect |
| 209. C3×C5 | #915 | semidirect |
| 210. C3×C5 | #918 | semidirect |
| 233. C32 | #4061 | semidirect |
| 253. C5 | #63951 | semidirect |
| 262. C3 | #91524 | semidirect |
| 263. C3 | #91804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊D15 | 2 |
| #10624196 | 2 |
| C3×#6718 | 2 |
| C3×C5×#215 | 2 |
| #10623808 | 2 |
| #10623805 | 2 |
| #10623797 | 2 |
| #91804 | 3 |
| #91524 | 3 |
| #63951 | 5 |