Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
321 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C2×#3718 | C2 | semidirect |
| 5. #63565 | C2 | semidirect |
| 70. C22×C32 | Q16 | semidirect |
| 136. C22×C3 | #216 | semidirect |
| 137. C22×C3 | #216 | semidirect |
| 152. C32 | #451 | semidirect |
| 180. C22 | #3718 | semidirect |
| 188. C3 | #5050 | semidirect |
| 189. C3 | #5228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| C3×#924 | 2 |
| C2×#3718 | 2 |
| #63657 | 2 |
| #63565 | 2 |
| #5228 | 3 |
| #5050 | 3 |