Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1099 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 1099 conjugacy classes of subgroups — too many to draw. Only its 223 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 |
|---|---|---|
| 3. C2×C4⋊#1088 | C2 | direct (N × H) |
| 7. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 8. C22×#1084 | C4 | semidirect |
| 9. C2×C4×#272 | C4 | semidirect |
| 11. C4⋊#1088 | C22 | direct (N × H) |
| 20. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 21. C2×#1084 | C2×C4 | semidirect |
| 22. C4×#272 | C2×C4 | semidirect |
| 30. C22×H(3,𝔽3) | C4⋊C4 | semidirect |
| 32. C2×#272 | C4⋊C4 | semidirect |
| 38. C4×H(3,𝔽3) | C22×C4 | semidirect |
| 39. #1084 | C22×C4 | semidirect |
| 54. C2×H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 56. #272 | C2×C4⋊C4 | semidirect |
| 84. H(3,𝔽3) | C22×C4⋊C4 | semidirect |
| 116. C22×C4 | #1088 | semidirect |
| 148. C2×C4 | C2×#1088 | semidirect |
| 164. C22 | C4⋊#1088 | direct (N × H) |
| 168. C4 | C22×#1088 | semidirect |
| 174. C2 | C2×C4⋊#1088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1088 | 2 |
| C22×C4×#272 | 2 |
| C2×C4⋊#1088 | 2 |
| C22×C3×C4⋊C4 | 9 |