Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
258 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 66 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. #63646⋊C3 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 4. #10589433 | C3 | semidirect |
| 16. #63646 | C2×C3 | semidirect |
| 17. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 136. H(3,𝔽3) | #359 | semidirect |
| 205. C32 | #4567 | semidirect |
| 206. C32 | C3×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#135 | 2 |
| #63646⋊C3 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589433 | 3 |
| C3×#4567 | 3 |