Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
366 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 107 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. #64096 | C2 | semidirect |
| 4. C32×#106 | C2 | semidirect |
| 5. C8×C3⋊Dic3 | C2 | semidirect |
| 6. #63637 | C2 | semidirect |
| 20. #3744 | C4 | semidirect |
| 24. C3×#106 | D3 | semidirect |
| 39. #634 | C2×C4 | semidirect |
| 40. C32×C8 | C2×C4 | semidirect |
| 65. C3⋊Dic3 | SD16 | semidirect |
| 69. #106 | C3⋊D3 | semidirect |
| 85. C3×C8 | C4×D3 | semidirect |
| 114. C32 | C4×SD16 | semidirect |
| 128. C8 | C4×C3⋊D3 | semidirect |
| 144. C3 | #4852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744 | 2 |
| #64102 | 2 |
| #64096 | 2 |
| C32×#106 | 2 |
| C8×C3⋊Dic3 | 2 |
| #63637 | 2 |
| #63636 | 2 |
| #4852 | 3 |