Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
190 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #91231 | C3 | direct (N × H) |
| 8. C3×C3⋊#170 | C4 | semidirect |
| 31. C3⋊#170 | C3×C4 | semidirect |
| 61. C32×C5 | #97 | semidirect |
| 101. C3×C5 | #803 | semidirect |
| 102. C3×C5 | C3×#97 | semidirect |
| 118. C32 | #4002 | semidirect |
| 132. C5 | C3×#803 | semidirect |
| 138. C3 | C3×#4002 | semidirect |
| 139. C3 | #91231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#170 | 2 |
| C32×C4×Dic5 | 2 |
| #91231 | 3 |
| C3×#4002 | 3 |
| C3×#803 | 5 |