Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11721746 | C2 | semidirect |
| 3. C3×C9×#102 | C2 | semidirect |
| 4. #11720576 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. #11720538 | C2 | semidirect |
| 7. #11720528 | C2 | semidirect |
| 30. C9×#102 | D3 | semidirect |
| 91. C3×#102 | D9 | semidirect |
| 190. #102 | C3⋊D9 | semidirect |
| 192. C3×C9 | #490 | semidirect |
| 271. C9 | #4764 | semidirect |
| 310. C3 | #10588444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| #11721746 | 2 |
| C3×C9×#102 | 2 |
| #11720576 | 2 |
| #11720543 | 2 |
| #11720538 | 2 |
| #11720528 | 2 |
| #10592463 | 3 |
| #10588444 | 3 |