Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
380 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. C2×C3×C9×SD16 | C2 | semidirect |
| 2. C3×#63505 | C2 | semidirect |
| 4. C3×#63464 | C2 | semidirect |
| 5. C3×#63394 | C2 | semidirect |
| 6. C3×#63391 | C2 | semidirect |
| 7. C3×#63372 | C2 | semidirect |
| 9. #10588857 | C3 | direct (N × H) |
| 33. C2×C9×SD16 | C2×C3 | semidirect |
| 34. #63505 | C2×C3 | semidirect |
| 36. #63464 | C2×C3 | semidirect |
| 37. #63394 | C2×C3 | semidirect |
| 38. #63391 | C2×C3 | semidirect |
| 39. #63372 | C2×C3 | semidirect |
| 104. C2×C3×SD16 | D9 | semidirect |
| 221. C2×SD16 | C3×D9 | semidirect |
| 226. C3×C9 | #471 | semidirect |
| 318. C9 | C3×#471 | semidirect |
| 355. C3 | #10588857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×SD16 | 2 |
| C3×#63505 | 2 |
| C3×#63495 | 2 |
| C3×#63464 | 2 |
| C3×#63394 | 2 |
| C3×#63391 | 2 |
| C3×#63372 | 2 |
| C3×#5177 | 3 |
| #10588857 | 3 |