Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
794 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 200 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×#926 | C2 | semidirect |
| 3. #63974 | C2 | semidirect |
| 4. #63894 | C2 | semidirect |
| 8. C2×C4⋊(C3⋊D3) | C4 | semidirect |
| 10. C2×#624 | C22 | semidirect |
| 12. C3×C4⋊Dic3 | C22 | semidirect |
| 13. C3×C4×Dic3 | C22 | semidirect |
| 14. #3722 | C22 | semidirect |
| 18. #926 | D3 | semidirect |
| 24. C22×C3⋊D3 | C2×C4 | semidirect |
| 26. C2×C32×C4 | C2×C4 | semidirect |
| 28. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 47. C4⋊Dic3 | C2×D3 | semidirect |
| 48. C4×Dic3 | C2×D3 | semidirect |
| 72. C2×C3×C4 | C4×D3 | semidirect |
| 110. C32 | #518 | semidirect |
| 118. C2×C4 | #624 | semidirect |
| 137. C3 | #5521 | 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 |
| C3×#926 | 2 |
| #63974 | 2 |
| #63894 | 2 |
| #5521 | 3 |