Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
230 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 31. C3×C3⋊C8 | Q8 | semidirect |
| 83. C3⋊C8 | Dic6 | semidirect |
| 112. C32 | #498 | semidirect |
| 137. C3 | #4680 | semidirect |
| 138. C3 | #5080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64078 | 2 |
| C3×#869 | 2 |
| C3×C4×C3⋊C8 | 2 |
| #63573 | 2 |
| #5080 | 3 |
| #4680 | 3 |