Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
296 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 65 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. C3×Q16×D9 | C2 | semidirect |
| 3. #11720567 | C2 | semidirect |
| 4. C9×#828 | C2 | semidirect |
| 5. #11720240 | C2 | semidirect |
| 6. #11720234 | C2 | semidirect |
| 7. D9×C3⋊C16 | C2 | semidirect |
| 12. C3×C9×Q16 | C22 | semidirect |
| 17. C3×Dic36 | C22 | semidirect |
| 19. C3⋊(C9⋊C16) | C22 | semidirect |
| 20. C9×C3⋊C16 | C22 | semidirect |
| 28. Q16×D9 | D3 | semidirect |
| 63. C9×Q16 | C2×D3 | semidirect |
| 70. Dic36 | C2×D3 | semidirect |
| 92. #828 | D9 | direct (N × H) |
| 126. C3×D9 | SD32 | semidirect |
| 134. C3×Q16 | C2×D9 | semidirect |
| 151. C3⋊C16 | C2×D9 | semidirect |
| 178. C3×C9 | C2×SD32 | semidirect |
| 213. D9 | #828 | direct (N × H) |
| 218. Q16 | D3×D9 | semidirect |
| 246. C9 | C2×#828 | semidirect |
| 277. C3 | D9×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q16×D9 | 2 |
| D9×D24 | 2 |
| #11720567 | 2 |
| C9×#828 | 2 |
| #11720240 | 2 |
| #11720234 | 2 |
| D9×C3⋊C16 | 2 |
| D3×#828 | 3 |
| D9×SD32 | 3 |