Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
564 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 111 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. C32×C22⋊Q8 | C2 | semidirect |
| 3. C2×#3755 | C2 | semidirect |
| 4. #63657 | C2 | semidirect |
| 5. #63636 | C2 | semidirect |
| 8. C2×C32×Q8 | C22 | semidirect |
| 14. C32×C4⋊C4 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 19. C3×C22⋊Q8 | D3 | semidirect |
| 40. C2×C3×Q8 | C2×D3 | semidirect |
| 46. C3×C4⋊C4 | C2×D3 | semidirect |
| 52. C22×C32 | SD16 | semidirect |
| 64. C22⋊Q8 | C3⋊D3 | semidirect |
| 88. C2×Q8 | C2×C3⋊D3 | semidirect |
| 96. C4⋊C4 | C2×C3⋊D3 | semidirect |
| 100. C22×C3 | #215 | semidirect |
| 110. C32 | #450 | semidirect |
| 137. C22 | #3755 | semidirect |
| 143. C3 | #5046 | 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 |
| C32×C22⋊Q8 | 2 |
| C2×#3755 | 2 |
| #63657 | 2 |
| #63636 | 2 |
| #5046 | 3 |