Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
798 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 271 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. C22×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. #64116 | C2 | direct (N × H) |
| 5. C2×#3743 | C2 | semidirect |
| 6. C2×C8×C3⋊D3 | C2 | semidirect |
| 15. C32×M16 | C22 | semidirect |
| 19. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. #3743 | C22 | semidirect |
| 21. C8×C3⋊D3 | C22 | semidirect |
| 23. C2×C3×M16 | D3 | semidirect |
| 51. C3×M16 | C2×D3 | semidirect |
| 70. C2×M16 | C3⋊D3 | semidirect |
| 89. C2×C32 | #131 | semidirect |
| 100. M16 | C2×C3⋊D3 | semidirect |
| 115. C32 | C2×#131 | semidirect |
| 132. C2×C3 | #907 | semidirect |
| 144. C3 | C2×#907 | semidirect |
| 147. C2 | #64116 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C2×C32×M16 | 2 |
| C22×C3⋊(C3⋊C8) | 2 |
| #64116 | 2 |
| C2×#3743 | 2 |
| C2×C8×C3⋊D3 | 2 |
| C2×#907 | 3 |