Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
1288 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 1288 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 |
|---|---|---|
| 3. C33×C4⋊C4 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 5. #88857 | C2 | semidirect |
| 13. C4×C3⋊(C3⋊D3) | C4 | semidirect |
| 16. C32×C4⋊C4 | D3 | semidirect |
| 24. C33×C4 | C2×C4 | semidirect |
| 26. C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 38. C3⋊(C3⋊D3) | C4⋊C4 | direct (N × H) |
| 41. C3×C4⋊C4 | C3⋊D3 | semidirect |
| 49. C32×C4 | C4×D3 | semidirect |
| 53. C33 | C2×C4⋊C4 | semidirect |
| 69. C4⋊C4 | C3⋊(C3⋊D3) | direct (N × H) |
| 75. C3×C4 | C4×C3⋊D3 | semidirect |
| 78. C32 | D3×C4⋊C4 | semidirect |
| 97. C4 | C4×C3⋊(C3⋊D3) | semidirect |
| 98. C3 | C4⋊C4×C3⋊D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊D3) | 2 |
| C33×C4⋊C4 | 2 |
| C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #88857 | 2 |
| C4⋊C4×C3⋊D3 | 3 |