Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
222 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 64 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. H(3,𝔽3)×M32 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 4. #10589381 | C3 | semidirect |
| 16. C32×M32 | D3 | semidirect |
| 17. C32×M32 | C2×C3 | semidirect |
| 18. C2×C3⋊(C3⋊C16) | C2×C3 | semidirect |
| 122. M32 | (C3⋊D3)⋊C3 | semidirect |
| 124. H(3,𝔽3) | #350 | semidirect |
| 186. C32 | #4515 | semidirect |
| 187. C32 | C3×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64110⋊C3 | 2 |
| H(3,𝔽3)×M32 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| #10589381 | 3 |
| C3×#4515 | 3 |