Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C3×Dic3⋊C8 | C2 | semidirect |
| 6. #5119 | C3 | direct (N × H) |
| 23. Dic3⋊C8 | C2×C3 | semidirect |
| 116. C32 | #424 | semidirect |
| 142. C3 | #5119 | direct (N × H) |
| 143. C3 | C3×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C3×#926 | 2 |
| C22×C3×C3⋊C8 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#424 | 3 |
| #5119 | 3 |