Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
218 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 80 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×C3⋊C16 | C2 | semidirect |
| 3. #63544 | C2 | direct (N × H) |
| 10. C3×C3⋊C16 | C22 | semidirect |
| 14. C2×C3⋊C16 | D3 | semidirect |
| 36. C3⋊C16 | C2×D3 | semidirect |
| 62. C2×C32 | M32 | semidirect |
| 83. C32 | C2×M32 | semidirect |
| 94. C2×C3 | #798 | semidirect |
| 105. C3 | C2×#798 | semidirect |
| 107. C2 | #63544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D3 | 2 |
| C2×C3×C3⋊C16 | 2 |
| #63544 | 2 |
| C2×#798 | 3 |