Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
472 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 90 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. #11722642 | C2 | semidirect |
| 2. 3−1+2×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #63498⋊C3 | C2 | semidirect |
| 4. #63495⋊C3 | C2 | semidirect |
| 5. #63396⋊C3 | C2 | semidirect |
| 6. #63384⋊C3 | C2 | semidirect |
| 7. #63382⋊C3 | C2 | semidirect |
| 9. #10588881 | C3 | semidirect |
| 31. #63716 | C2×C3 | semidirect |
| 36. C9×AGL(1,ℤ/8) | C2×C3 | semidirect |
| 37. #63498 | C2×C3 | semidirect |
| 38. #63495 | C2×C3 | semidirect |
| 39. #63396 | C2×C3 | semidirect |
| 40. #63384 | C2×C3 | semidirect |
| 41. #63382 | C2×C3 | semidirect |
| 254. AGL(1,ℤ/8) | AGL(1,ℤ/9) | semidirect |
| 259. 3−1+2 | #454 | semidirect |
| 359. C9 | C3×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722642 | 2 |
| 3−1+2×AGL(1,ℤ/8) | 2 |
| #63498⋊C3 | 2 |
| #63495⋊C3 | 2 |
| #63396⋊C3 | 2 |
| #63384⋊C3 | 2 |
| #63382⋊C3 | 2 |
| C3×#5201 | 3 |
| #10588881 | 3 |