Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
125 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 125 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 9. #889 | C3 | direct (N × H) |
| 88. C32 | #125 | semidirect |
| 114. C3 | #889 | direct (N × H) |
| 115. C3 | C3×#125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C4×Dic3 | 2 |
| C3×#125 | 3 |
| #889 | 3 |