Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
940 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 211 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. C2×#88543 | C2 | semidirect |
| 3. #11721813 | C2 | semidirect |
| 4. #11720576 | C2 | semidirect |
| 5. #11720571 | C2 | semidirect |
| 13. C2×#6226 | C22 | semidirect |
| 16. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 18. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 74. C22×C3×C9 | SD16 | semidirect |
| 166. C22×C9 | #214 | semidirect |
| 177. C3×C9 | #450 | semidirect |
| 241. C22×C3 | #3672 | semidirect |
| 254. C9 | #5218 | semidirect |
| 286. C22 | #88543 | semidirect |
| 292. C3 | #10588897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4×C9 | 2 |
| C2×#88543 | 2 |
| #11721813 | 2 |
| #11720576 | 2 |
| #11720571 | 2 |
| #10592917 | 3 |
| #10588897 | 3 |