Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
679 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 679 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 |
|---|---|---|
| 2. C82×3−1+2 | C2 | semidirect |
| 3. #10588132⋊C3 | C2 | semidirect |
| 5. #11773687 | C3 | semidirect |
| 16. C82×C9 | C2×C3 | semidirect |
| 17. #10588132 | C2×C3 | semidirect |
| 41. C8×3−1+2 | M16 | semidirect |
| 90. C8×C9 | C3×M16 | semidirect |
| 94. C82 | AGL(1,ℤ/9) | semidirect |
| 124. 3−1+2 | #1455 | semidirect |
| 158. C9 | C3×#1455 | semidirect |
| 164. C8 | #3663⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3663⋊C3 | 2 |
| C82×3−1+2 | 2 |
| #10588132⋊C3 | 2 |
| C3×#68050 | 3 |
| #11773687 | 3 |