Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
199 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 76 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. #63371⋊C3 | C2 | semidirect |
| 3. C2×3−1+2⋊C16 | C2 | semidirect |
| 5. #10588238 | C3 | semidirect |
| 18. #63371 | C2×C3 | semidirect |
| 19. C2×C9⋊C16 | C2×C3 | semidirect |
| 120. 3−1+2 | #350 | semidirect |
| 165. C9 | C3×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#131 | 2 |
| #63371⋊C3 | 2 |
| C2×3−1+2⋊C16 | 2 |
| C3×#4561 | 3 |
| #10588238 | 3 |