Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
930 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 930 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×#88418 | C2 | direct (N × H) |
| 15. #88418 | C22 | direct (N × H) |
| 59. C22×C3×C9 | Q16 | semidirect |
| 101. C2×C3×C9 | C2×Q16 | semidirect |
| 133. C22×C9 | #216 | semidirect |
| 146. C3×C9 | C22×Q16 | semidirect |
| 177. C2×C9 | C2×#216 | semidirect |
| 190. C22×C3 | Dic36 | semidirect |
| 207. C9 | C22×#216 | semidirect |
| 220. C2×C3 | C2×Dic36 | semidirect |
| 224. C22 | #88418 | direct (N × H) |
| 231. C3 | C22×Dic36 | semidirect |
| 233. C2 | C2×#88418 | 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×Dic18 | 2 |
| C22×C9×C3⋊C8 | 2 |
| C2×#88418 | 2 |
| C22×#3719 | 3 |
| C22×Dic36 | 3 |