Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
1688 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 268 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. C3×#6308 | C2 | semidirect |
| 3. C33×Dic6 | C2 | semidirect |
| 4. #10620148 | C2 | semidirect |
| 19. #6308 | D3 | semidirect |
| 21. C32×Dic6 | D3 | semidirect |
| 25. C3⋊(C3⋊(C3⋊D3)) | Q8 | semidirect |
| 41. C34 | C2×Q8 | semidirect |
| 50. C3×Dic6 | C3⋊D3 | semidirect |
| 75. C33 | D3×Q8 | semidirect |
| 76. C33 | D3×Q8 | semidirect |
| 87. Dic6 | C3⋊(C3⋊D3) | semidirect |
| 109. C32 | #3797 | semidirect |
| 110. C32 | Q8×C3⋊D3 | semidirect |
| 128. C3 | #89019 | semidirect |
| 129. C3 | Q8×C3⋊(C3⋊D3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊(C3⋊(C3⋊D3)) | 2 |
| C3×#6308 | 2 |
| C33×Dic6 | 2 |
| #10620148 | 2 |
| #10620144 | 2 |
| Q8×C3⋊(C3⋊D3) | 3 |
| #89019 | 3 |