Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #11720913 | C2 | semidirect |
| 5. #11720277 | C2 | semidirect |
| 6. C3⋊C8×Dic9 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 13. #88543 | C4 | semidirect |
| 43. #6226 | C2×C4 | semidirect |
| 49. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 91. C3×Dic9 | SD16 | semidirect |
| 204. Dic9 | #214 | semidirect |
| 212. C3×C9 | C4×SD16 | semidirect |
| 304. C9 | C4×#214 | semidirect |
| 343. C3 | #10588438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×D4×Dic9 | 2 |
| #11720913 | 2 |
| C9×#832 | 2 |
| #11720277 | 2 |
| C3⋊C8×Dic9 | 2 |
| #11720265 | 2 |
| #10591401 | 3 |
| #10588438 | 3 |