Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
1848 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 335 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×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C33×C22⋊C4 | C2 | semidirect |
| 4. #88864 | C2 | semidirect |
| 5. #88859 | C2 | semidirect |
| 9. C22×C3⋊(C3⋊D3) | C4 | semidirect |
| 12. C2×C33×C4 | C22 | semidirect |
| 13. C2×C3⋊(C3⋊Dic3) | C22 | semidirect |
| 17. C32×C22⋊C4 | D3 | semidirect |
| 21. C22×C33 | C2×C4 | semidirect |
| 26. C2×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 36. C2×C32×C4 | C2×D3 | semidirect |
| 43. C3⋊(C3⋊D3) | C22⋊C4 | direct (N × H) |
| 46. C3×C22⋊C4 | C3⋊D3 | semidirect |
| 50. C22×C32 | C4×D3 | semidirect |
| 60. C33 | C2×C22⋊C4 | semidirect |
| 66. C2×C3×C4 | C2×C3⋊D3 | semidirect |
| 78. C22⋊C4 | C3⋊(C3⋊D3) | direct (N × H) |
| 80. C22×C3 | C4×C3⋊D3 | semidirect |
| 89. C32 | D3×C22⋊C4 | semidirect |
| 97. C2×C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 109. C22 | C4×C3⋊(C3⋊D3) | semidirect |
| 113. C3 | C22⋊C4×C3⋊D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊(C3⋊D3) | 2 |
| C2×C4×C3⋊(C3⋊D3) | 2 |
| C33×C22⋊C4 | 2 |
| #88864 | 2 |
| #88859 | 2 |
| C22⋊C4×C3⋊D3 | 3 |