Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
268 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 71 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. C5×#3743 | C2 | semidirect |
| 3. C3×#6705 | C2 | semidirect |
| 4. C3×C8×D15 | C2 | semidirect |
| 5. #10623819 | C2 | semidirect |
| 6. #10623818 | C2 | semidirect |
| 7. #10623817 | C2 | semidirect |
| 24. #6705 | D3 | semidirect |
| 25. C8×D15 | D3 | semidirect |
| 46. #3743 | D5 | semidirect |
| 133. C32×C5 | #131 | semidirect |
| 207. C3×C5 | #901 | semidirect |
| 208. C3×C5 | #907 | semidirect |
| 230. C32 | #4053 | semidirect |
| 252. C5 | #63804 | semidirect |
| 261. C3 | #91266 | semidirect |
| 262. C3 | #91268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624223 | 2 |
| C5×#3743 | 2 |
| C3×#6705 | 2 |
| C3×C8×D15 | 2 |
| #10623819 | 2 |
| #10623818 | 2 |
| #10623817 | 2 |
| #91268 | 3 |
| #91266 | 3 |
| #63804 | 5 |