Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×#869 | C2 | semidirect |
| 3. C2×#3719 | C2 | semidirect |
| 5. C3×#803 | C2 | semidirect |
| 25. #869 | D3 | semidirect |
| 27. #803 | D3 | semidirect |
| 131. C32 | #497 | semidirect |
| 159. C3 | #4715 | semidirect |
| 160. C3 | #5086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64084 | 2 |
| C3×#869 | 2 |
| C2×#3719 | 2 |
| C2×#3717 | 2 |
| C3×#803 | 2 |
| #5086 | 3 |
| #4715 | 3 |