Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
329 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 66 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×#897 | C2 | semidirect |
| 3. C2×#3718 | C2 | semidirect |
| 4. C2×#3717 | C2 | semidirect |
| 5. #63636 | C2 | semidirect |
| 6. C3×#810 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 32. #897 | D3 | semidirect |
| 36. #810 | D3 | semidirect |
| 210. C32 | #452 | semidirect |
| 258. C3 | #4808 | semidirect |
| 259. C3 | #5047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3799 | 2 |
| C3×#897 | 2 |
| C2×#3718 | 2 |
| C2×#3717 | 2 |
| #63636 | 2 |
| C3×#810 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #5047 | 3 |
| #4808 | 3 |