Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
604 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 198 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×C32×Dic3 | C2 | semidirect |
| 3. C33×C22⋊C4 | C2 | semidirect |
| 4. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C32×C4⋊Dic3 | C2 | semidirect |
| 7. C3×#886 | C3 | direct (N × H) |
| 18. C22×C3×Dic3 | C2×C3 | semidirect |
| 22. C32×C22⋊C4 | D3 | semidirect |
| 23. C32×C22⋊C4 | C2×C3 | semidirect |
| 24. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 25. C3×C4⋊Dic3 | C2×C3 | semidirect |
| 35. #886 | C32 | direct (N × H) |
| 59. C22×Dic3 | C2×C32 | semidirect |
| 63. C3×C22⋊C4 | C3×D3 | semidirect |
| 64. C3×C22⋊C4 | C2×C32 | semidirect |
| 65. (C2×D3)⋊C4 | C2×C32 | semidirect |
| 66. C4⋊Dic3 | C2×C32 | semidirect |
| 88. C33 | #123 | semidirect |
| 120. C22⋊C4 | C32×D3 | semidirect |
| 142. C32 | #886 | direct (N × H) |
| 143. C32 | C3×#123 | semidirect |
| 171. C3 | C3×#886 | direct (N × H) |
| 172. C3 | C32×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#67 | 2 |
| C22×C32×Dic3 | 2 |
| C33×C22⋊C4 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C32×C4⋊Dic3 | 2 |
| C32×#123 | 3 |
| C3×#886 | 3 |