Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1155 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1155 conjugacy classes of subgroups — too many to draw. Only its 113 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. C22⋊C4×#272 | C2 | semidirect |
| 3. H(3,𝔽3)×#99 | C2 | semidirect |
| 4. #11720580 | C2 | semidirect |
| 5. #11720524 | C2 | semidirect |
| 7. C23×#272 | C4 | semidirect |
| 10. C2×#6235 | C4 | semidirect |
| 14. C2×C4⋊#272 | C4 | semidirect |
| 16. C2×C4×#272 | C4 | semidirect |
| 17. C22⋊C4×H(3,𝔽3) | C22 | semidirect |
| 18. #88552 | C22 | semidirect |
| 22. C32×#99 | D3 | semidirect |
| 25. C23×H(3,𝔽3) | C2×C4 | semidirect |
| 33. C22×#272 | C2×C4 | semidirect |
| 38. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 42. C2×#1084 | C2×C4 | semidirect |
| 59. C32×C22⋊C4 | C2×D3 | semidirect |
| 92. C23×C32 | C4×D3 | semidirect |
| 105. C2×C32×C4 | C4×D3 | semidirect |
| 122. #272 | #99 | direct (N × H) |
| 173. #99 | #272 | direct (N × H) |
| 174. H(3,𝔽3) | C2×#99 | semidirect |
| 239. C22⋊C4 | C2×#272 | semidirect |
| 280. C32 | D3×#99 | semidirect |
| 290. C23 | C4×#272 | semidirect |
| 302. C2×C4 | C4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#272 | 2 |
| C22⋊C4×#272 | 2 |
| H(3,𝔽3)×#99 | 2 |
| #11720580 | 2 |
| #11720524 | 2 |
| C3×D3×#99 | 3 |