Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
979 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 979 conjugacy classes of subgroups — too many to draw. Only its 155 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⋊#1088 | C2 | semidirect |
| 3. D4×#1088 | C2 | semidirect |
| 4. #11722448 | C2 | semidirect |
| 6. C22×#1088 | C22 | semidirect |
| 7. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 8. C2×#6235 | C4 | semidirect |
| 9. D4×#272 | C4 | semidirect |
| 11. C2×C4⋊#272 | C4 | semidirect |
| 14. C22⋊#1088 | C22 | semidirect |
| 15. C4⋊#1088 | C22 | semidirect |
| 16. C4×#1088 | C22 | semidirect |
| 18. C23×H(3,𝔽3) | C2×C4 | semidirect |
| 20. C22×#272 | C2×C4 | semidirect |
| 21. C22×#272 | C2×C4 | semidirect |
| 26. D4×H(3,𝔽3) | C2×C4 | semidirect |
| 27. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 28. #6235 | C2×C4 | semidirect |
| 29. C2×#1084 | C2×C4 | semidirect |
| 30. C4⋊#272 | C2×C4 | semidirect |
| 31. C4×#272 | C2×C4 | semidirect |
| 114. H(3,𝔽3) | #518 | semidirect |
| 154. C2×D4 | #1088 | semidirect |
| 192. C23 | C2×#1088 | semidirect |
| 195. D4 | C2×#1088 | semidirect |
| 201. C2×C4 | C2×#1088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#272 | 2 |
| C2×C22⋊#1088 | 2 |
| D4×#1088 | 2 |
| #11722448 | 2 |
| C3×#518 | 9 |