Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 108 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×C32×Dic10 | C2 | semidirect |
| 3. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 4. C3×Dic3⋊Dic5 | C2 | semidirect |
| 7. #91390 | C3 | direct (N × H) |
| 19. C2×C3×Dic10 | D3 | semidirect |
| 20. C2×C3×Dic10 | C2×C3 | semidirect |
| 22. C5×C4⋊Dic3 | C2×C3 | semidirect |
| 25. Dic3⋊Dic5 | C2×C3 | semidirect |
| 30. C2×C3×D15 | Q8 | semidirect |
| 39. C3×C4⋊Dic3 | D5 | semidirect |
| 65. C2×Dic10 | C3×D3 | semidirect |
| 81. C2×D15 | C3×Q8 | semidirect |
| 104. C4⋊Dic3 | C3×D5 | semidirect |
| 106. C32×C5 | C22⋊Q8 | semidirect |
| 169. C3×C5 | #946 | semidirect |
| 170. C3×C5 | C3×C22⋊Q8 | semidirect |
| 194. C32 | #4043 | semidirect |
| 213. C5 | C3×#946 | semidirect |
| 223. C3 | #91390 | direct (N × H) |
| 224. C3 | C3×#4043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C2×C32×Dic10 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×#6667 | 2 |
| C3×#4043 | 3 |
| #91390 | 3 |
| C3×#946 | 5 |