Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1852 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 1852 conjugacy classes of subgroups — too many to draw. Only its 452 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 |
|---|---|---|
| 4. C2×#88798 | C2 | direct (N × H) |
| 15. #88798 | C22 | direct (N × H) |
| 57. C22×C33 | Q16 | semidirect |
| 97. C2×C33 | C2×Q16 | semidirect |
| 121. C22×C32 | #216 | semidirect |
| 122. C22×C32 | #216 | semidirect |
| 139. C33 | C22×Q16 | semidirect |
| 166. C2×C32 | C2×#216 | semidirect |
| 167. C2×C32 | C2×#216 | semidirect |
| 181. C22×C3 | #3718 | semidirect |
| 182. C22×C3 | #3756 | semidirect |
| 196. C32 | C22×#216 | semidirect |
| 197. C32 | C22×#216 | semidirect |
| 210. C2×C3 | C2×#3718 | semidirect |
| 211. C2×C3 | C2×#3756 | semidirect |
| 214. C22 | #88798 | direct (N × H) |
| 221. C3 | C22×#3718 | semidirect |
| 222. C3 | C22×#3756 | semidirect |
| 223. C2 | C2×#88798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#634 | 2 |
| C22×C32×Dic6 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C2×#88798 | 2 |
| C22×#3756 | 3 |
| C22×#3718 | 3 |