Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
324 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. C4⋊(C3⋊#157) | C2 | direct (N × H) |
| 8. C2×C33×C4 | C4 | semidirect |
| 9. C2×C3×C3⋊Dic3 | C4 | semidirect |
| 10. C3×C4×C3⋊D3 | C4 | semidirect |
| 22. C33×C4 | C2×C4 | semidirect |
| 23. C3×C3⋊Dic3 | C2×C4 | semidirect |
| 31. C2×C32×C4 | Dic3 | semidirect |
| 32. C2×C3⋊Dic3 | Dic3 | semidirect |
| 33. C4×C3⋊D3 | Dic3 | semidirect |
| 38. C2×C33 | C4⋊C4 | semidirect |
| 40. C3×C3⋊D3 | C4⋊C4 | semidirect |
| 61. C32×C4 | C2×Dic3 | semidirect |
| 62. C3⋊Dic3 | C2×Dic3 | semidirect |
| 65. C33 | C2×C4⋊C4 | semidirect |
| 73. C2×C3×C4 | #157 | semidirect |
| 83. C2×C32 | C4⋊Dic3 | semidirect |
| 85. C3⋊D3 | C4⋊Dic3 | semidirect |
| 108. C3×C4 | C2×#157 | semidirect |
| 113. C32 | C2×C4⋊Dic3 | semidirect |
| 120. C2×C4 | C3⋊#157 | semidirect |
| 128. C2×C3 | C4⋊#157 | semidirect |
| 140. C4 | C2×C3⋊#157 | semidirect |
| 143. C3 | C2×C4⋊#157 | semidirect |
| 147. C2 | C4⋊(C3⋊#157) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊#157 | 2 |
| C2×C3×C4×C3⋊D3 | 2 |
| C4⋊(C3⋊#157) | 2 |
| C2×C4⋊#157 | 3 |
| C2×C4⋊Dic3 | 9 |