Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 108 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. #63464⋊C3 | C2 | semidirect |
| 3. C4×C8×3−1+2 | C2 | semidirect |
| 4. #63372⋊C3 | C2 | semidirect |
| 5. #63364⋊C3 | C2 | semidirect |
| 7. #10588380 | C3 | semidirect |
| 13. D72⋊C3 | C4 | semidirect |
| 14. #3664⋊C3 | C4 | semidirect |
| 17. Dic36⋊C3 | C4 | semidirect |
| 24. #63464 | C2×C3 | semidirect |
| 26. C4×C8×C9 | C2×C3 | semidirect |
| 27. #63372 | C2×C3 | semidirect |
| 28. #63364 | C2×C3 | semidirect |
| 60. D72 | C3×C4 | semidirect |
| 61. #3664 | C3×C4 | semidirect |
| 64. Dic36 | C3×C4 | semidirect |
| 153. C4×C8 | AGL(1,ℤ/9) | semidirect |
| 154. 3−1+2 | #443 | semidirect |
| 209. C9 | C3×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63467⋊C3 | 2 |
| #63464⋊C3 | 2 |
| C4×C8×3−1+2 | 2 |
| #63372⋊C3 | 2 |
| #63364⋊C3 | 2 |
| C3×#4700 | 3 |
| #10588380 | 3 |