Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 84 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. C3×#869 | C2 | semidirect |
| 3. C2×#3715 | C2 | semidirect |
| 4. C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 19. #869 | D3 | semidirect |
| 30. C3⋊(C3⋊C8) | D4 | semidirect |
| 51. C32×C4 | SD16 | semidirect |
| 97. C3×C4 | #214 | semidirect |
| 98. C3×C4 | #215 | semidirect |
| 102. C32 | #492 | semidirect |
| 123. C4 | #3715 | semidirect |
| 126. C3 | #5076 | semidirect |
| 127. C3 | #5085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#874 | 2 |
| C3×#869 | 2 |
| C2×#3715 | 2 |
| C4×C3⋊(C3⋊C8) | 2 |
| #5085 | 3 |
| #5076 | 3 |