Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
426 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 81 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. A4×Dic6 | C2 | direct (N × H) |
| 4. C23×Dic6 | C3 | semidirect |
| 16. C22×Dic6 | C2×C3 | semidirect |
| 21. C2×C3×A4 | Q8 | semidirect |
| 48. C2×Dic6 | A4 | direct (N × H) |
| 53. C3×A4 | C2×Q8 | semidirect |
| 66. C23×C3 | C3×Q8 | semidirect |
| 70. C2×A4 | Dic6 | direct (N × H) |
| 91. Dic6 | C2×A4 | direct (N × H) |
| 122. C22×C3 | C2×C3×Q8 | semidirect |
| 125. A4 | C2×Dic6 | direct (N × H) |
| 137. C23 | C3×Dic6 | semidirect |
| 162. C2×C3 | Q8×A4 | semidirect |
| 171. C22 | C2×C3×Dic6 | semidirect |
| 179. C3 | C2×Q8×A4 | semidirect |
| 183. C2 | A4×Dic6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×A4 | 2 |
| C2×Dic3×A4 | 2 |
| A4×Dic6 | 2 |
| C23×Dic6 | 3 |
| C2×Q8×A4 | 3 |
| C2×C3×Dic6 | 4 |