Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
647 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 647 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11722366 | C2 | direct (N × H) |
| 24. C2×C9×A4 | Q8 | semidirect |
| 55. C9×A4 | C2×Q8 | semidirect |
| 76. C23×C9 | Dic6 | semidirect |
| 78. C2×C22⋊C9 | Dic6 | semidirect |
| 130. C22×C9 | C2×Dic6 | semidirect |
| 132. C22⋊C9 | C2×Dic6 | semidirect |
| 152. C2×A4 | Dic18 | semidirect |
| 177. C2×C9 | A4⋊Q8 | semidirect |
| 204. A4 | C2×Dic18 | semidirect |
| 213. C9 | C2×A4⋊Q8 | semidirect |
| 217. C23 | #6226 | semidirect |
| 246. C22 | C2×#6226 | semidirect |
| 257. C2 | #11722366 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9×A4 | 2 |
| C2×C9⋊SL(2,ℤ/4) | 2 |
| #11722366 | 2 |
| C2×#64259 | 3 |
| C2×(C22⋊C9)⋊Q8 | 3 |
| C2×#63486 | 3 |
| C2×#6226 | 4 |