Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
390 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 4. C32×C4×C8 | C2 | semidirect |
| 5. #63642 | C2 | semidirect |
| 6. C8×C3⋊Dic3 | C2 | semidirect |
| 7. #63630 | C2 | semidirect |
| 18. #3743 | C4 | semidirect |
| 19. C8×C3⋊D3 | C4 | semidirect |
| 23. C3×C4×C8 | D3 | semidirect |
| 64. C4×C8 | C3⋊D3 | semidirect |
| 98. C32 | #405 | semidirect |
| 121. C3 | #4689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C2×C8×C3⋊D3 | 2 |
| #64081 | 2 |
| C32×C4×C8 | 2 |
| #63642 | 2 |
| C8×C3⋊Dic3 | 2 |
| #63630 | 2 |
| #4689 | 3 |