Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 67 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. C3×#6762 | C2 | semidirect |
| 3. C2×C3×C3⋊#170 | C2 | semidirect |
| 4. #10623983 | C2 | semidirect |
| 5. #10623982 | C2 | semidirect |
| 6. #10623981 | C2 | semidirect |
| 7. #10623980 | C2 | semidirect |
| 25. #6762 | D3 | semidirect |
| 26. C2×C3⋊#170 | D3 | semidirect |
| 141. C32×C5 | #131 | semidirect |
| 221. C3×C5 | #901 | semidirect |
| 222. C3×C5 | #907 | semidirect |
| 248. C32 | #4131 | semidirect |
| 272. C5 | #63817 | semidirect |
| 281. C3 | #91927 | semidirect |
| 282. C3 | #91929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624165 | 2 |
| C3×#6762 | 2 |
| C2×C3×C3⋊#170 | 2 |
| #10623983 | 2 |
| #10623982 | 2 |
| #10623981 | 2 |
| #10623980 | 2 |
| #91929 | 3 |
| #91927 | 3 |
| #63817 | 5 |