Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
604 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 130 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×#63383 | C2 | semidirect |
| 7. D9×#100 | C3 | direct (N × H) |
| 15. C3×C9×M16 | C22 | semidirect |
| 16. C3×#3667 | C22 | semidirect |
| 25. M16×D9 | C2×C3 | semidirect |
| 27. C9×#100 | C2×C3 | semidirect |
| 28. #63391 | C2×C3 | semidirect |
| 29. #63383 | C2×C3 | semidirect |
| 67. C9×M16 | C22×C3 | semidirect |
| 68. #3667 | C22×C3 | semidirect |
| 90. C3×#100 | D9 | direct (N × H) |
| 134. C3×D9 | #100 | direct (N × H) |
| 153. C3×M16 | C2×D9 | semidirect |
| 191. #100 | C3×D9 | direct (N × H) |
| 192. C3×C9 | C2×#100 | semidirect |
| 241. D9 | C3×#100 | direct (N × H) |
| 251. M16 | C2×C3×D9 | semidirect |
| 283. C9 | C2×C3×#100 | semidirect |
| 327. C3 | D9×#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D9 | 2 |
| C3×M16×D9 | 2 |
| C3×C9×#100 | 2 |
| C3×#63391 | 2 |
| C3×#63383 | 2 |
| C3×D3×#100 | 3 |
| D9×#100 | 3 |