Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
190 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 100. C32 | #499 | semidirect |
| 120. C3 | #4683 | semidirect |
| 121. C3 | #4858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63869 | 2 |
| #63644 | 2 |
| C3×#817 | 2 |
| C3×C8×Dic3 | 2 |
| #63575 | 2 |
| #4858 | 3 |
| #4683 | 3 |