Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
496 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 126 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×M16×D9 | C2 | semidirect |
| 3. C3×C9×#100 | C2 | semidirect |
| 4. C3×#63391 | C2 | semidirect |
| 5. C3×#63382 | C2 | semidirect |
| 7. #10588425 | C3 | direct (N × H) |
| 25. M16×D9 | C2×C3 | semidirect |
| 27. C9×#100 | C2×C3 | semidirect |
| 28. #63391 | C2×C3 | semidirect |
| 29. #63382 | C2×C3 | semidirect |
| 86. C3×#100 | D9 | semidirect |
| 177. #100 | C3×D9 | semidirect |
| 178. C3×C9 | #413 | semidirect |
| 257. C9 | C3×#413 | semidirect |
| 293. C3 | #10588425 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3699 | 2 |
| C3×M16×D9 | 2 |
| C3×C9×#100 | 2 |
| C3×#63391 | 2 |
| C3×#63382 | 2 |
| C3×#4745 | 3 |
| #10588425 | 3 |