Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
570 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 155 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×C32×M16 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #63647 | C2 | semidirect |
| 14. C2×C32×C8 | C22 | semidirect |
| 16. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 18. C2×C3×M16 | D3 | semidirect |
| 45. C2×C3×C8 | C2×D3 | semidirect |
| 54. C2×C3⋊D3 | M16 | semidirect |
| 61. C2×M16 | C3⋊D3 | semidirect |
| 92. C2×C8 | C2×C3⋊D3 | semidirect |
| 104. C32 | #407 | semidirect |
| 135. C3 | #5126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊D3 | 2 |
| C2×C32×M16 | 2 |
| C2×#3748 | 2 |
| #63647 | 2 |
| #5126 | 3 |