Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1155 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1155 conjugacy classes of subgroups — too many to draw. Only its 173 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×C22⋊C4×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#88552 | C2 | semidirect |
| 4. #11720524 | C2 | direct (N × H) |
| 7. C23×#272 | C4 | semidirect |
| 13. C2×#6235 | C4 | semidirect |
| 16. C22×#1084 | C4 | semidirect |
| 18. C22⋊C4×H(3,𝔽3) | C22 | semidirect |
| 20. #88552 | C22 | semidirect |
| 22. C2×C32×C22⋊C4 | D3 | semidirect |
| 36. C22×#272 | C2×C4 | semidirect |
| 47. C2×#1084 | C2×C4 | semidirect |
| 62. C32×C22⋊C4 | C2×D3 | semidirect |
| 124. C2×H(3,𝔽3) | #99 | semidirect |
| 180. C2×C22⋊C4 | #272 | semidirect |
| 182. H(3,𝔽3) | C2×#99 | semidirect |
| 235. C2×C32 | #806 | semidirect |
| 252. C22⋊C4 | C2×#272 | semidirect |
| 295. C32 | C2×#806 | semidirect |
| 367. C2 | #11720524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6235 | 2 |
| C2×C22⋊C4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| #11720524 | 2 |
| C2×C3×#806 | 3 |