Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
410 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 2. C2×C3×Dic3⋊C4 | C2 | semidirect |
| 3. C32×#95 | C2 | semidirect |
| 5. #4676 | C3 | direct (N × H) |
| 14. C2×Dic3⋊C4 | C2×C3 | semidirect |
| 16. C3×#95 | D3 | semidirect |
| 17. C3×#95 | C2×C3 | semidirect |
| 50. #95 | C3×D3 | semidirect |
| 104. C32 | #396 | semidirect |
| 135. C3 | #4676 | direct (N × H) |
| 136. C3 | C3×#396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×(C2×D3)⋊C4 | 2 |
| C2×C3×Dic3⋊C4 | 2 |
| C32×#95 | 2 |
| C3×#396 | 3 |
| #4676 | 3 |