Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
604 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 186 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. C2×C32×C4×D3 | C2 | semidirect |
| 3. C33×C22⋊C4 | C2 | semidirect |
| 4. C32×#217 | C2 | semidirect |
| 5. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C32×C4⋊Dic3 | C2 | semidirect |
| 7. C32×Dic3⋊C4 | C2 | semidirect |
| 9. C3×#883 | C3 | direct (N × H) |
| 22. C2×C3×C4×D3 | C2×C3 | semidirect |
| 28. C32×C22⋊C4 | D3 | semidirect |
| 29. C32×C22⋊C4 | C2×C3 | semidirect |
| 30. C3×#217 | C2×C3 | semidirect |
| 31. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 32. C3×C4⋊Dic3 | C2×C3 | semidirect |
| 33. C3×Dic3⋊C4 | C2×C3 | semidirect |
| 47. #883 | C32 | direct (N × H) |
| 77. C2×C4×D3 | C2×C32 | semidirect |
| 83. C3×C22⋊C4 | C3×D3 | semidirect |
| 84. C3×C22⋊C4 | C2×C32 | semidirect |
| 85. #217 | C2×C32 | semidirect |
| 86. (C2×D3)⋊C4 | C2×C32 | semidirect |
| 87. C4⋊Dic3 | C2×C32 | semidirect |
| 88. Dic3⋊C4 | C2×C32 | semidirect |
| 120. C33 | #123 | semidirect |
| 162. C22⋊C4 | C32×D3 | semidirect |
| 194. C32 | #883 | direct (N × H) |
| 195. C32 | C3×#123 | semidirect |
| 232. C3 | C3×#883 | direct (N × H) |
| 233. 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 |
| C2×C32×C4×D3 | 2 |
| C33×C22⋊C4 | 2 |
| C32×#217 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C32×C4⋊Dic3 | 2 |
| C32×Dic3⋊C4 | 2 |
| C32×#123 | 3 |
| C3×#883 | 3 |