Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
354 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 98 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×#63454 | C2 | semidirect |
| 3. C3×C9×#107 | C2 | semidirect |
| 4. C3×#63380 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 6. C3×#63369 | C2 | semidirect |
| 7. C3×#63367 | C2 | semidirect |
| 9. #10588565 | C3 | direct (N × H) |
| 29. #63454 | C2×C3 | semidirect |
| 31. C9×#107 | C2×C3 | semidirect |
| 32. #63380 | C2×C3 | semidirect |
| 33. (C2×D9)⋊C8 | C2×C3 | semidirect |
| 34. #63369 | C2×C3 | semidirect |
| 35. #63367 | C2×C3 | semidirect |
| 95. C3×#107 | D9 | semidirect |
| 201. #107 | C3×D9 | semidirect |
| 206. C3×C9 | #482 | semidirect |
| 296. C9 | C3×#482 | semidirect |
| 338. C3 | #10588565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63457 | 2 |
| C3×#63454 | 2 |
| C3×C9×#107 | 2 |
| C3×#63380 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C3×#63369 | 2 |
| C3×#63367 | 2 |
| C3×#4885 | 3 |
| #10588565 | 3 |