Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
514 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 1. C3×#63713 | C2 | semidirect |
| 2. C3×C9×#124 | C2 | semidirect |
| 3. C3×#63495 | C2 | semidirect |
| 4. C3×#63394 | C2 | semidirect |
| 5. C3×#63364 | C2 | semidirect |
| 7. #10588742 | C3 | direct (N × H) |
| 22. #63713 | C2×C3 | semidirect |
| 26. C9×#124 | C2×C3 | semidirect |
| 27. #63495 | C2×C3 | semidirect |
| 28. #63394 | C2×C3 | semidirect |
| 29. #63364 | C2×C3 | semidirect |
| 84. C3×#124 | D9 | semidirect |
| 180. #124 | C3×D9 | semidirect |
| 183. C3×C9 | #454 | semidirect |
| 264. C9 | C3×#454 | semidirect |
| 299. C3 | #10588742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63713 | 2 |
| C3×C9×#124 | 2 |
| C3×#63495 | 2 |
| C3×#63394 | 2 |
| C3×#63364 | 2 |
| C3×#5062 | 3 |
| #10588742 | 3 |