Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
700 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 1. #11721840 | C2 | semidirect |
| 2. C2×#88544 | C2 | semidirect |
| 3. C2×#88525 | C2 | semidirect |
| 4. #11721749 | C2 | semidirect |
| 5. C3×C9×#102 | C2 | semidirect |
| 6. #11720537 | C2 | semidirect |
| 7. #11720528 | C2 | semidirect |
| 34. C9×#102 | D3 | semidirect |
| 51. C4⋊(C3⋊D9) | D4 | semidirect |
| 97. C3⋊Dic9 | D8 | semidirect |
| 106. C3×#102 | D9 | semidirect |
| 217. #102 | C3⋊D9 | semidirect |
| 218. C3×C9 | #459 | semidirect |
| 311. C9 | #4786 | semidirect |
| 357. C3 | #10588466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| C2×#88544 | 2 |
| C2×#88525 | 2 |
| #11721749 | 2 |
| C3×C9×#102 | 2 |
| #11720537 | 2 |
| #11720528 | 2 |
| #10592485 | 3 |
| #10588466 | 3 |