Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1176 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. C22×#6296 | C2 | semidirect |
| 3. C22×C3⋊#622 | C2 | semidirect |
| 4. C2×#88937 | C2 | direct (N × H) |
| 10. C2×#6296 | C22 | semidirect |
| 13. C2×C3⋊#622 | C22 | semidirect |
| 14. #88937 | C22 | direct (N × H) |
| 28. #6296 | C23 | semidirect |
| 31. C3⋊#622 | C23 | semidirect |
| 54. C22×C33 | SD16 | semidirect |
| 100. C2×C33 | C2×SD16 | semidirect |
| 134. C22×C32 | #214 | semidirect |
| 156. C33 | C22×SD16 | semidirect |
| 198. C2×C32 | C2×#214 | semidirect |
| 226. C22×C3 | #3775 | semidirect |
| 244. C32 | C22×#214 | semidirect |
| 267. C2×C3 | C2×#3775 | semidirect |
| 272. C22 | #88937 | direct (N × H) |
| 281. C3 | C22×#3775 | semidirect |
| 283. C2 | C2×#88937 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6296 | 2 |
| C22×C3×#625 | 2 |
| C22×C3⋊#622 | 2 |
| C2×#88937 | 2 |
| C22×#3775 | 3 |
| C22×#214 | 9 |