Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
442 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 138 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 |
|---|---|---|
| 5. #5230 | C3 | direct (N × H) |
| 25. C2×C3×Dic3 | Q8 | semidirect |
| 67. C2×Dic3 | C3×Q8 | semidirect |
| 92. C32 | #395 | semidirect |
| 117. C3 | #5230 | direct (N × H) |
| 118. C3 | C3×#395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C2×C3×Dic3⋊C4 | 2 |
| C3×C3⋊#95 | 2 |
| C3×#395 | 3 |
| #5230 | 3 |