Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#835 | C2 | semidirect |
| 5. C3×#803 | C2 | semidirect |
| 7. #5055 | C3 | direct (N × H) |
| 21. #869 | C2×C3 | semidirect |
| 25. #835 | C2×C3 | semidirect |
| 27. #803 | C2×C3 | semidirect |
| 142. C32 | #489 | semidirect |
| 175. C3 | #5055 | direct (N × H) |
| 176. C3 | C3×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#124 | 2 |
| C3×#869 | 2 |
| C3×#835 | 2 |
| C3×#832 | 2 |
| C3×#803 | 2 |
| C3×#489 | 3 |
| #5055 | 3 |