Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
852 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 292 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. C2×#3674⋊C3 | C2 | direct (N × H) |
| 6. C22×#3674 | C3 | semidirect |
| 14. #3674⋊C3 | C22 | direct (N × H) |
| 23. C2×#3674 | C2×C3 | semidirect |
| 57. #3674 | C22×C3 | semidirect |
| 59. C22×3−1+2 | Q16 | semidirect |
| 100. C2×3−1+2 | C2×Q16 | semidirect |
| 128. C22×C9 | C3×Q16 | semidirect |
| 141. 3−1+2 | C22×Q16 | semidirect |
| 166. C2×C9 | C2×C3×Q16 | semidirect |
| 191. C9 | C22×C3×Q16 | semidirect |
| 206. C22 | #3674⋊C3 | direct (N × H) |
| 214. C2 | C2×#3674⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×3−1+2 | 2 |
| C22×3−1+2⋊Q8 | 2 |
| C2×#3674⋊C3 | 2 |
| C22×3−1+2⋊C8 | 2 |
| C22×C3×#216 | 3 |
| C22×#3674 | 3 |