Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
1818 conjugacy classes of subgroups; only the 608 normal subgroups are shown.
This group has 1818 conjugacy classes of subgroups — too many to draw. Only its 608 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. C22×C3×Dic6 | C2 | semidirect |
| 3. C22×#627 | C2 | semidirect |
| 5. C2×#3797 | C2 | direct (N × H) |
| 12. C2×C3×Dic6 | C22 | semidirect |
| 13. C2×#627 | C22 | semidirect |
| 15. #3797 | C22 | direct (N × H) |
| 22. C22×Dic6 | D3 | semidirect |
| 24. C22×C3⋊D3 | Q8 | semidirect |
| 30. C3×Dic6 | C23 | semidirect |
| 31. #627 | C23 | semidirect |
| 48. C2×Dic6 | C2×D3 | semidirect |
| 49. C22×C32 | C2×Q8 | semidirect |
| 51. C2×C3⋊D3 | C2×Q8 | semidirect |
| 78. Dic6 | C22×D3 | semidirect |
| 79. C2×C32 | C22×Q8 | semidirect |
| 81. C3⋊D3 | C22×Q8 | semidirect |
| 93. C22×C3 | D3×Q8 | semidirect |
| 105. C32 | C23×Q8 | semidirect |
| 118. C2×C3 | C2×D3×Q8 | semidirect |
| 124. C22 | #3797 | direct (N × H) |
| 130. C3 | C22×D3×Q8 | semidirect |
| 132. C2 | C2×#3797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊D3 | 2 |
| C22×C3×Dic6 | 2 |
| C22×#627 | 2 |
| C22×#624 | 2 |
| C2×#3797 | 2 |
| C22×D3×Q8 | 3 |