Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
850 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 257 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×#88427 | C2 | direct (N × H) |
| 15. #88427 | C22 | direct (N × H) |
| 57. C22×C3×C9 | Q16 | semidirect |
| 97. C2×C3×C9 | C2×Q16 | semidirect |
| 127. C22×C9 | #216 | semidirect |
| 139. C3×C9 | C22×Q16 | semidirect |
| 168. C2×C9 | C2×#216 | semidirect |
| 181. C22×C3 | #3674 | semidirect |
| 197. C9 | C22×#216 | semidirect |
| 210. C2×C3 | C2×#3674 | semidirect |
| 214. C22 | #88427 | direct (N × H) |
| 221. C3 | C22×#3674 | semidirect |
| 223. C2 | C2×#88427 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Dic6 | 2 |
| C22×C3×Dic18 | 2 |
| C22×C3⋊(C9⋊C8) | 2 |
| C2×#88427 | 2 |
| C22×#3718 | 3 |
| C22×#3674 | 3 |