Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
502 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×#63498 | C2 | semidirect |
| 3. C3×#63471 | C2 | semidirect |
| 4. C3×C9×#100 | C2 | semidirect |
| 5. C3×#63384 | C2 | semidirect |
| 7. #10588426 | C3 | direct (N × H) |
| 13. C2×C3×Dic18 | C22 | semidirect |
| 14. C3×C9×M16 | C22 | semidirect |
| 16. C3×C4×Dic9 | C22 | semidirect |
| 25. #63498 | C2×C3 | semidirect |
| 26. #63471 | C2×C3 | semidirect |
| 28. C9×#100 | C2×C3 | semidirect |
| 29. #63384 | C2×C3 | semidirect |
| 63. C2×Dic18 | C22×C3 | semidirect |
| 65. C9×M16 | C22×C3 | semidirect |
| 67. C4×Dic9 | C22×C3 | semidirect |
| 87. C3×#100 | D9 | semidirect |
| 143. C3×M16 | C2×D9 | semidirect |
| 177. #100 | C3×D9 | semidirect |
| 178. C3×C9 | #455 | semidirect |
| 230. M16 | C2×C3×D9 | semidirect |
| 257. C9 | C3×#455 | semidirect |
| 293. C3 | #10588426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63710 | 2 |
| C3×#63498 | 2 |
| C3×#63471 | 2 |
| C3×C9×#100 | 2 |
| C3×#63384 | 2 |
| C3×#4746 | 3 |
| #10588426 | 3 |