Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
270 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #479 | semidirect |
| 124. C3 | #4799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic3 | 2 |
| #64099 | 2 |
| C32×#103 | 2 |
| #63662 | 2 |
| #63644 | 2 |
| #63641 | 2 |
| #63634 | 2 |
| #4799 | 3 |