Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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. #63506 | C2 | semidirect |
| 3. C2×#3674 | C2 | semidirect |
| 6. C2×Dic36 | C2 | semidirect |
| 7. #63375 | C2 | semidirect |
| 116. C9 | #497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×SD16 | 2 |
| #63506 | 2 |
| C2×#3674 | 2 |
| #63498 | 2 |
| C2×#3672 | 2 |
| C2×Dic36 | 2 |
| #63375 | 2 |
| #5167 | 3 |