Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
407 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 96 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. C2×#3672⋊C3 | C2 | semidirect |
| 3. #63486⋊C3 | C2 | semidirect |
| 4. C2×#3667⋊C3 | C2 | semidirect |
| 5. #63392⋊C3 | C2 | semidirect |
| 6. #63368⋊C3 | C2 | semidirect |
| 7. #63366⋊C3 | C2 | semidirect |
| 9. #10588718 | C3 | semidirect |
| 32. C2×#3672 | C2×C3 | semidirect |
| 33. #63486 | C2×C3 | semidirect |
| 34. C2×#3667 | C2×C3 | semidirect |
| 35. #63392 | C2×C3 | semidirect |
| 36. #63368 | C2×C3 | semidirect |
| 37. #63366 | C2×C3 | semidirect |
| 53. 3−1+2⋊C8 | D4 | semidirect |
| 155. C9⋊C8 | C3×D4 | semidirect |
| 232. 3−1+2 | #468 | semidirect |
| 321. C9 | C3×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#121 | 2 |
| C2×#3672⋊C3 | 2 |
| #63486⋊C3 | 2 |
| C2×#3667⋊C3 | 2 |
| #63392⋊C3 | 2 |
| #63368⋊C3 | 2 |
| #63366⋊C3 | 2 |
| C3×#5042 | 3 |
| #10588718 | 3 |