Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
182 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 56 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. C22×C3×Q16 | C3 | semidirect |
| 4. A4×Q16 | C3 | direct (N × H) |
| 18. C22×Q16 | C32 | semidirect |
| 30. C3×Q16 | A4 | direct (N × H) |
| 33. C3×A4 | Q16 | direct (N × H) |
| 64. Q16 | C3×A4 | direct (N × H) |
| 69. C22×C3 | C3×Q16 | semidirect |
| 70. A4 | C3×Q16 | direct (N × H) |
| 95. C22 | C32×Q16 | semidirect |
| 101. C3 | A4×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×A4 | 2 |
| C3×C8×A4 | 2 |
| C22×C3×Q16 | 3 |
| A4×Q16 | 3 |
| C32×Q16 | 4 |