Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
210 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 1. C2×#3746 | C2 | semidirect |
| 3. C2×C3×C3⋊C16 | C2 | semidirect |
| 4. #63548 | C2 | direct (N × H) |
| 11. #3746 | C22 | semidirect |
| 14. C3×C3⋊C16 | C22 | semidirect |
| 22. C2×C3⋊C16 | D3 | semidirect |
| 53. C3⋊C16 | C2×D3 | semidirect |
| 88. C2×C32 | SD32 | semidirect |
| 115. C32 | C2×SD32 | semidirect |
| 128. C2×C3 | #800 | semidirect |
| 129. C2×C3 | #827 | semidirect |
| 140. C3 | C2×#800 | semidirect |
| 141. C3 | C2×#827 | semidirect |
| 143. C2 | #63548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| C2×C3×D24 | 2 |
| C2×C3×C3⋊C16 | 2 |
| #63548 | 2 |
| C2×#827 | 3 |
| C2×#800 | 3 |