Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 500 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×#3675 | C2 | semidirect |
| 4. C3×#63502 | C2 | semidirect |
| 5. C2×C3×#3673 | C2 | semidirect |
| 6. C2×C3×D72 | C2 | semidirect |
| 7. C3×#63375 | C2 | semidirect |
| 9. #10588856 | C3 | direct (N × H) |
| 31. C2×C9×SD16 | C2×C3 | semidirect |
| 32. #63509 | C2×C3 | semidirect |
| 33. C2×#3675 | C2×C3 | semidirect |
| 34. #63502 | C2×C3 | semidirect |
| 35. C2×#3673 | C2×C3 | semidirect |
| 36. C2×D72 | C2×C3 | semidirect |
| 37. #63375 | C2×C3 | semidirect |
| 53. C3×C8×C9 | D4 | semidirect |
| 54. C3×C9⋊C8 | D4 | semidirect |
| 100. C2×C3×SD16 | D9 | semidirect |
| 153. C8×C9 | C3×D4 | semidirect |
| 154. C9⋊C8 | C3×D4 | semidirect |
| 220. C2×SD16 | C3×D9 | semidirect |
| 226. C3×C9 | #496 | semidirect |
| 266. C3×C8 | #611 | semidirect |
| 325. C9 | C3×#496 | semidirect |
| 342. C8 | C3×#611 | semidirect |
| 368. C3 | #10588856 | 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×#3675 | 2 |
| C3×#63502 | 2 |
| C2×C3×#3673 | 2 |
| C2×C3×D72 | 2 |
| C3×#63375 | 2 |
| C3×#5176 | 3 |
| #10588856 | 3 |