Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 35. C32×C8 | Q8 | semidirect |
| 36. C3⋊(C3⋊C8) | Q8 | semidirect |
| 73. C3×C8 | Dic6 | semidirect |
| 98. C32 | #501 | semidirect |
| 108. C8 | #634 | semidirect |
| 121. C3 | #4876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64099 | 2 |
| #64097 | 2 |
| C32×#107 | 2 |
| #63644 | 2 |
| #63642 | 2 |
| #63635 | 2 |
| #63634 | 2 |
| #4876 | 3 |