Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
326 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 132 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. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 4. #63362⋊C3 | C2 | semidirect |
| 5. C4×3−1+2⋊C8 | C2 | semidirect |
| 7. #10588678 | C3 | semidirect |
| 23. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 24. #63362 | C2×C3 | semidirect |
| 25. C4×C9⋊C8 | C2×C3 | semidirect |
| 138. 3−1+2 | #433 | semidirect |
| 187. C9 | C3×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#117 | 2 |
| #63389⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| #63362⋊C3 | 2 |
| C4×3−1+2⋊C8 | 2 |
| C3×#5000 | 3 |
| #10588678 | 3 |