Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
840 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 263 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 |
|---|---|---|
| 1. C33×C4⋊C4 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 6. #88857 | C2 | semidirect |
| 7. C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 16. C32×C4⋊C4 | D3 | semidirect |
| 45. C3×C4⋊C4 | C3⋊D3 | semidirect |
| 63. C33 | #126 | semidirect |
| 77. C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 92. C32 | #898 | semidirect |
| 114. C3 | #64107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊C4 | 2 |
| #88859 | 2 |
| C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #88857 | 2 |
| C4×C3⋊(C3⋊Dic3) | 2 |
| #64107 | 3 |