Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1290 conjugacy classes of subgroups; only the 431 normal subgroups are shown.
This group has 1290 conjugacy classes of subgroups — too many to draw. Only its 431 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×#88521 | C2 | direct (N × H) |
| 11. #88521 | C22 | direct (N × H) |
| 39. C22×C3×C9 | Q16 | semidirect |
| 65. C2×C3×C9 | C2×Q16 | semidirect |
| 84. C22×C9 | Dic12 | semidirect |
| 92. C3×C9 | C22×Q16 | semidirect |
| 109. C2×C9 | C2×Dic12 | semidirect |
| 117. C22×C3 | Dic36 | semidirect |
| 128. C9 | C22×Dic12 | semidirect |
| 136. C2×C3 | C2×Dic36 | semidirect |
| 140. C22 | #88521 | direct (N × H) |
| 145. C3 | C22×Dic36 | semidirect |
| 147. C2 | C2×#88521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6226 | 2 |
| C22×C3×C8×C9 | 2 |
| C2×#88521 | 2 |
| C22×#3746 | 3 |
| C22×Dic36 | 3 |