Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11721707 | C2 | semidirect |
| 3. C3×C9×#97 | C2 | semidirect |
| 4. #11720543 | C2 | semidirect |
| 19. C9×#97 | D3 | semidirect |
| 52. C3×#97 | D9 | semidirect |
| 101. #97 | C3⋊D9 | semidirect |
| 102. C3×C9 | #490 | semidirect |
| 142. C9 | #4713 | semidirect |
| 162. C3 | #10588394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| #11721707 | 2 |
| C3×C9×#97 | 2 |
| #11720543 | 2 |
| #10592412 | 3 |
| #10588394 | 3 |