Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
259 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 70 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×C16×H(3,𝔽3) | C2 | semidirect |
| 3. #63645⋊C3 | C2 | semidirect |
| 4. #10589375 | C3 | semidirect |
| 10. #3745⋊C3 | C4 | semidirect |
| 15. C2×C32×C16 | D3 | semidirect |
| 16. C2×C32×C16 | C2×C3 | semidirect |
| 17. #63645 | C2×C3 | semidirect |
| 36. #3745 | C3×C4 | semidirect |
| 120. C2×C16 | (C3⋊D3)⋊C3 | semidirect |
| 122. H(3,𝔽3) | #357 | semidirect |
| 189. C32 | #4509 | semidirect |
| 190. C32 | C3×#357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| #63645⋊C3 | 2 |
| #10589375 | 3 |
| C3×#4509 | 3 |