Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11721791 | C2 | semidirect |
| 2. D8×C3⋊D9 | C2 | semidirect |
| 3. C3×C9×D16 | C2 | semidirect |
| 4. #11720564 | C2 | semidirect |
| 5. #11720563 | C2 | semidirect |
| 6. #11720508 | C2 | semidirect |
| 7. #11720506 | C2 | semidirect |
| 13. C3×C9×D8 | C22 | semidirect |
| 18. #88521 | C22 | semidirect |
| 19. C3×C9×C16 | C22 | semidirect |
| 20. C3⋊(C9⋊C16) | C22 | semidirect |
| 30. C9×D16 | D3 | semidirect |
| 62. C9×D8 | C2×D3 | semidirect |
| 68. C9×C16 | C2×D3 | semidirect |
| 82. C3×D16 | D9 | semidirect |
| 125. C3×D8 | C2×D9 | semidirect |
| 138. C3×C16 | C2×D9 | semidirect |
| 163. D16 | C3⋊D9 | semidirect |
| 165. C3×C9 | #509 | semidirect |
| 205. D8 | C2×C3⋊D9 | semidirect |
| 208. C16 | C2×C3⋊D9 | semidirect |
| 226. C9 | #4911 | semidirect |
| 256. C3 | #10588591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721791 | 2 |
| D8×C3⋊D9 | 2 |
| C3×C9×D16 | 2 |
| #11720564 | 2 |
| #11720563 | 2 |
| #11720508 | 2 |
| #11720506 | 2 |
| #10592610 | 3 |
| #10588591 | 3 |