Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
760 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #11721813 | C2 | semidirect |
| 3. C2×#88524 | C2 | semidirect |
| 4. C2×#88521 | C2 | semidirect |
| 5. C3×C9×C22⋊C8 | C2 | semidirect |
| 6. #11720543 | C2 | semidirect |
| 7. #11720539 | C2 | semidirect |
| 36. C9×C22⋊C8 | D3 | semidirect |
| 111. C3×C22⋊C8 | D9 | semidirect |
| 223. C22⋊C8 | C3⋊D9 | semidirect |
| 224. C3×C9 | #452 | semidirect |
| 315. C9 | #4733 | semidirect |
| 358. C3 | #10588415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88736 | 2 |
| #11721813 | 2 |
| C2×#88524 | 2 |
| C2×#88521 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720543 | 2 |
| #11720539 | 2 |
| #10592432 | 3 |
| #10588415 | 3 |