Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
214 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 214 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×#870 | C2 | semidirect |
| 3. C32×C4×C8 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #4697 | C3 | direct (N × H) |
| 18. #870 | C2×C3 | semidirect |
| 22. C3×C4×C8 | D3 | semidirect |
| 23. C3×C4×C8 | C2×C3 | semidirect |
| 25. #816 | C2×C3 | semidirect |
| 62. C4×C8 | C3×D3 | semidirect |
| 109. C32 | #488 | semidirect |
| 134. C3 | #4697 | direct (N × H) |
| 135. C3 | C3×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#875 | 2 |
| C3×#870 | 2 |
| C32×C4×C8 | 2 |
| C3×#821 | 2 |
| C3×#816 | 2 |
| C3×#488 | 3 |
| #4697 | 3 |