Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
424 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×M16×3−1+2 | C2 | semidirect |
| 2. #63492⋊C3 | C2 | semidirect |
| 3. C2×D72⋊C3 | C2 | semidirect |
| 4. #63380⋊C3 | C2 | semidirect |
| 5. #63377⋊C3 | C2 | semidirect |
| 7. #10588817 | C3 | semidirect |
| 23. C2×C9×M16 | C2×C3 | semidirect |
| 24. #63492 | C2×C3 | semidirect |
| 25. C2×D72 | C2×C3 | semidirect |
| 26. #63380 | C2×C3 | semidirect |
| 27. #63377 | C2×C3 | semidirect |
| 39. C8×3−1+2 | D4 | semidirect |
| 114. C8×C9 | C3×D4 | semidirect |
| 165. C2×M16 | AGL(1,ℤ/9) | semidirect |
| 169. 3−1+2 | #469 | semidirect |
| 236. C9 | C3×#469 | semidirect |
| 248. C8 | #611⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×3−1+2 | 2 |
| #63492⋊C3 | 2 |
| C2×D72⋊C3 | 2 |
| #63380⋊C3 | 2 |
| #63377⋊C3 | 2 |
| C3×#5135 | 3 |
| #10588817 | 3 |