Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
178 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 78 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×Dic24 | C2 | direct (N × H) |
| 5. C2×Dic24 | C3 | direct (N × H) |
| 17. Dic24 | C2×C3 | direct (N × H) |
| 59. C2×C32 | Q32 | semidirect |
| 77. C32 | C2×Q32 | semidirect |
| 86. C2×C3 | Dic24 | direct (N × H) |
| 87. C2×C3 | C3×Q32 | semidirect |
| 95. C3 | C2×Dic24 | direct (N × H) |
| 96. C3 | C2×C3×Q32 | semidirect |
| 97. C2 | C3×Dic24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C32×C16 | 2 |
| C3×Dic24 | 2 |
| C2×C3×Q32 | 3 |
| C2×Dic24 | 3 |