Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 93 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×C9×#213 | C2 | semidirect |
| 3. C2×C3×#3673 | C2 | semidirect |
| 4. #11721043 | C2 | semidirect |
| 5. C2×#88422 | C2 | semidirect |
| 6. C2×#88417 | C2 | semidirect |
| 7. #11720271 | C2 | semidirect |
| 35. C2×#3673 | D3 | semidirect |
| 54. C9×C3⋊C8 | D4 | semidirect |
| 55. C3×C9⋊C8 | D4 | semidirect |
| 99. C3⋊Dic9 | D8 | semidirect |
| 110. C2×#213 | D9 | semidirect |
| 159. C9⋊C8 | #67 | semidirect |
| 236. C3×C9 | #493 | semidirect |
| 281. C3⋊C8 | #611 | semidirect |
| 345. C9 | #5151 | semidirect |
| 393. C3 | #10588831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721840 | 2 |
| C2×C9×#213 | 2 |
| C2×C3×#3673 | 2 |
| #11721043 | 2 |
| C2×#88422 | 2 |
| C2×#88417 | 2 |
| #11720271 | 2 |
| #10591484 | 3 |
| #10588831 | 3 |