Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
967 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 967 conjugacy classes of subgroups — too many to draw. Only its 167 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. #11722448 | C2 | direct (N × H) |
| 4. C2×C4⋊#1088 | C2 | semidirect |
| 5. C2×C4×#1088 | C2 | semidirect |
| 8. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 9. C22×#1084 | C4 | semidirect |
| 10. C2×C4×#272 | C4 | semidirect |
| 11. C2×C4×#272 | C4 | semidirect |
| 12. C2×C4×#272 | C4 | semidirect |
| 17. C4⋊#1088 | C22 | semidirect |
| 18. C4×#1088 | C22 | semidirect |
| 30. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 33. C2×#1084 | C2×C4 | semidirect |
| 36. C4×#272 | C2×C4 | semidirect |
| 37. C4×#272 | C2×C4 | semidirect |
| 91. C2×H(3,𝔽3) | #117 | semidirect |
| 94. #272 | #117 | semidirect |
| 137. H(3,𝔽3) | C2×#117 | semidirect |
| 191. C22×C4 | #1088 | semidirect |
| 244. C2×C4 | C2×#1088 | semidirect |
| 278. C2 | #11722448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#272 | 2 |
| C2×C22⋊#1088 | 2 |
| #11722448 | 2 |
| C2×C4⋊#1088 | 2 |
| C2×C4×#1088 | 2 |
| C2×C3×#117 | 9 |