Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10624219 | C2 | semidirect |
| 3. C5×#3746 | C2 | semidirect |
| 4. C3×#6706 | C2 | semidirect |
| 5. C3×#6705 | C2 | semidirect |
| 6. #10623826 | C2 | semidirect |
| 7. #10623823 | C2 | semidirect |
| 26. #6706 | D3 | semidirect |
| 27. #6705 | D3 | semidirect |
| 47. #3746 | D5 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 202. C3×C5 | #909 | semidirect |
| 203. C3×C5 | #915 | semidirect |
| 224. C32 | #4064 | semidirect |
| 243. C5 | #63800 | semidirect |
| 252. C3 | #91261 | semidirect |
| 253. C3 | #91278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624221 | 2 |
| #10624219 | 2 |
| C5×#3746 | 2 |
| C3×#6706 | 2 |
| C3×#6705 | 2 |
| #10623826 | 2 |
| #10623823 | 2 |
| #91278 | 3 |
| #91261 | 3 |
| #63800 | 5 |