Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
282 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 282 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 |
|---|---|---|
| 4. #63866 | C2 | semidirect |
| 5. C2×#3719 | C2 | semidirect |
| 6. C2×#3718 | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 181. C32 | #497 | semidirect |
| 217. C3 | #5060 | semidirect |
| 218. C3 | #5167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3754 | 2 |
| C3×#936 | 2 |
| C2×C3×#214 | 2 |
| #63866 | 2 |
| C2×#3719 | 2 |
| C2×#3718 | 2 |
| #63554 | 2 |
| #5167 | 3 |
| #5060 | 3 |