Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
182 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 182 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. #91233 | C3 | direct (N × H) |
| 17. C32×Dic5 | C8 | semidirect |
| 54. C3×Dic5 | C3⋊C8 | semidirect |
| 55. C3×Dic5 | C3×C8 | semidirect |
| 65. C32×C5 | C4⋊C8 | semidirect |
| 98. Dic5 | C3×C3⋊C8 | semidirect |
| 107. C3×C5 | C4⋊(C3⋊C8) | semidirect |
| 108. C3×C5 | C3×C4⋊C8 | semidirect |
| 127. C32 | #4004 | semidirect |
| 141. C5 | C3×C4⋊(C3⋊C8) | semidirect |
| 148. C3 | C3×#4004 | semidirect |
| 149. C3 | #91233 | 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 |
| #91233 | 3 |
| C3×#4004 | 3 |
| C3×C4⋊(C3⋊C8) | 5 |