Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×C3×Dic30 | C2 | semidirect |
| 3. C32×C5×C22⋊C4 | C2 | semidirect |
| 4. C3×#6719 | C2 | semidirect |
| 5. C3×#6714 | C2 | semidirect |
| 6. C3×#6714 | C2 | semidirect |
| 7. C3×C4×Dic15 | C2 | semidirect |
| 8. #91774 | C3 | direct (N × H) |
| 21. C2×Dic30 | C2×C3 | semidirect |
| 25. C3×C5×C22⋊C4 | D3 | semidirect |
| 26. C3×C5×C22⋊C4 | C2×C3 | semidirect |
| 27. #6719 | C2×C3 | semidirect |
| 28. #6714 | C2×C3 | semidirect |
| 29. #6714 | C2×C3 | semidirect |
| 30. C4×Dic15 | C2×C3 | semidirect |
| 50. C32×C22⋊C4 | D5 | semidirect |
| 85. C5×C22⋊C4 | C3×D3 | semidirect |
| 137. C3×C22⋊C4 | C3×D5 | semidirect |
| 138. C3×C22⋊C4 | D15 | semidirect |
| 144. C32×C5 | #124 | semidirect |
| 224. C22⋊C4 | C3×D15 | semidirect |
| 227. C3×C5 | #885 | semidirect |
| 228. C3×C5 | C3×#124 | semidirect |
| 264. C32 | #4031 | semidirect |
| 288. C5 | C3×#885 | semidirect |
| 302. C3 | C3×#4031 | semidirect |
| 303. C3 | #91774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1220 | 2 |
| C2×C3×Dic30 | 2 |
| C32×C5×C22⋊C4 | 2 |
| C3×#6719 | 2 |
| C3×#6714 | 2 |
| C3×C4×Dic15 | 2 |
| #91774 | 3 |
| C3×#4031 | 3 |
| C3×#885 | 5 |