Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
286 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 134 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. #5118 | C3 | direct (N × H) |
| 24. Dic3⋊C8 | C2×C3 | semidirect |
| 64. C3×Dic3 | M16 | semidirect |
| 128. Dic3 | C3×M16 | semidirect |
| 129. C32 | #423 | semidirect |
| 158. C3 | #5118 | direct (N × H) |
| 159. C3 | C3×#423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C2×C3×C4×Dic3 | 2 |
| C2×C3×#208 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#423 | 3 |
| #5118 | 3 |