Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3674⋊C3 | C2 | semidirect |
| 5. #63394⋊C3 | C2 | semidirect |
| 6. #63382⋊C3 | C2 | semidirect |
| 7. #63381⋊C3 | C2 | semidirect |
| 9. #10588882 | C3 | semidirect |
| 36. C2×#3674 | C2×C3 | semidirect |
| 37. #63394 | C2×C3 | semidirect |
| 38. #63382 | C2×C3 | semidirect |
| 39. #63381 | C2×C3 | semidirect |
| 216. 3−1+2 | #473 | semidirect |
| 289. C9 | C3×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#137 | 2 |
| #63511⋊C3 | 2 |
| #11721693 | 2 |
| C2×#3674⋊C3 | 2 |
| #63394⋊C3 | 2 |
| #63382⋊C3 | 2 |
| #63381⋊C3 | 2 |
| C3×#5204 | 3 |
| #10588882 | 3 |