Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 173 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. #11721706 | C2 | semidirect |
| 3. C3×C9×C4⋊C8 | C2 | semidirect |
| 5. #11720541 | C2 | semidirect |
| 24. C9×C4⋊C8 | D3 | semidirect |
| 34. C4⋊(C3⋊D9) | Q8 | semidirect |
| 72. C3×C4⋊C8 | D9 | semidirect |
| 146. C4⋊C8 | C3⋊D9 | semidirect |
| 148. C3×C9 | #474 | semidirect |
| 209. C9 | #4846 | semidirect |
| 239. C3 | #10588530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C3⋊D9) | 2 |
| #11721706 | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720543 | 2 |
| #11720541 | 2 |
| #10592545 | 3 |
| #10588530 | 3 |