Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×C9×#204 | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 4. #11720930 | C2 | semidirect |
| 5. C2×#88425 | C2 | semidirect |
| 6. C2×#88423 | C2 | semidirect |
| 7. C8×C3⋊Dic9 | C2 | semidirect |
| 35. C2×#3664 | D3 | semidirect |
| 53. C3×C8×C9 | D4 | semidirect |
| 54. C3⋊(C9⋊C8) | D4 | semidirect |
| 93. C3⋊Dic9 | SD16 | semidirect |
| 107. C2×#204 | D9 | semidirect |
| 146. C8×C9 | #67 | semidirect |
| 214. C3×C9 | #492 | semidirect |
| 248. C3×C8 | #611 | semidirect |
| 302. C9 | #5175 | semidirect |
| 319. C8 | #6194 | semidirect |
| 341. C3 | #10588855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#204 | 2 |
| C2×C3×#3664 | 2 |
| #11721043 | 2 |
| #11720930 | 2 |
| C2×#88425 | 2 |
| C2×#88423 | 2 |
| C8×C3⋊Dic9 | 2 |
| #10590884 | 3 |
| #10588855 | 3 |