Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 4. C2×C3×#3674 | C2 | semidirect |
| 5. C3×#63394 | C2 | semidirect |
| 6. C3×#63382 | C2 | semidirect |
| 7. C3×#63381 | C2 | semidirect |
| 9. #10588882 | C3 | direct (N × H) |
| 36. C2×#3674 | C2×C3 | semidirect |
| 37. #63394 | C2×C3 | semidirect |
| 38. #63382 | C2×C3 | semidirect |
| 39. #63381 | C2×C3 | semidirect |
| 222. C3×C9 | #473 | semidirect |
| 310. C9 | C3×#473 | semidirect |
| 344. C3 | #10588882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#137 | 2 |
| C3×#63511 | 2 |
| C3×#63510 | 2 |
| C2×C3×#3674 | 2 |
| C3×#63394 | 2 |
| C3×#63382 | 2 |
| C3×#63381 | 2 |
| C3×#5204 | 3 |
| #10588882 | 3 |