Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
435 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 226 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 |
|---|---|---|
| 9. #5569 | C3 | direct (N × H) |
| 37. C32×Q8 | Q8 | semidirect |
| 91. C3×Q8 | Dic6 | semidirect |
| 92. C3×Q8 | C3×Q8 | semidirect |
| 146. C32 | #557 | semidirect |
| 148. Q8 | C3×Dic6 | semidirect |
| 174. C3 | #5569 | direct (N × H) |
| 175. C3 | C3×#557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#890 | 2 |
| C3×#888 | 2 |
| C3×#870 | 2 |
| C3×C4×Dic6 | 2 |
| C3×#557 | 3 |
| #5569 | 3 |