Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
554 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 3. C3×C3⋊#95 | C2 | semidirect |
| 5. #5211 | C3 | direct (N × H) |
| 8. C22×C32×C4 | C4 | semidirect |
| 18. C3⋊#95 | C2×C3 | semidirect |
| 38. C22×C3×C4 | Dic3 | semidirect |
| 39. C22×C3×C4 | C3×C4 | semidirect |
| 88. C22×C4 | C3×Dic3 | semidirect |
| 114. C32 | #381 | semidirect |
| 145. C3 | #5211 | direct (N × H) |
| 146. C3 | C3×#381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C4 | 2 |
| C2×C3×#217 | 2 |
| C3×C3⋊#95 | 2 |
| C3×#381 | 3 |
| #5211 | 3 |