Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 114 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×#63509 | C2 | semidirect |
| 3. C2×C3×#3674 | C2 | semidirect |
| 4. C3×#63498 | C2 | semidirect |
| 6. C2×C3×#3664 | C2 | semidirect |
| 7. C3×C8×Dic9 | C2 | semidirect |
| 9. #10588848 | C3 | direct (N × H) |
| 31. C2×C9×SD16 | C2×C3 | semidirect |
| 32. #63509 | C2×C3 | semidirect |
| 33. C2×#3674 | C2×C3 | semidirect |
| 34. #63498 | C2×C3 | semidirect |
| 36. C2×#3664 | C2×C3 | semidirect |
| 37. C8×Dic9 | C2×C3 | semidirect |
| 99. C2×C3×SD16 | D9 | semidirect |
| 214. C2×SD16 | C3×D9 | semidirect |
| 219. C3×C9 | #495 | semidirect |
| 312. C9 | C3×#495 | semidirect |
| 351. C3 | #10588848 | 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×#63509 | 2 |
| C2×C3×#3674 | 2 |
| C3×#63498 | 2 |
| C2×C3×#3673 | 2 |
| C2×C3×#3664 | 2 |
| C3×C8×Dic9 | 2 |
| C3×#5168 | 3 |
| #10588848 | 3 |