Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
296 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 61 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×D8×D9 | C2 | semidirect |
| 2. #11720822 | C2 | semidirect |
| 3. #11720564 | C2 | semidirect |
| 4. C9×#826 | C2 | semidirect |
| 5. #11720238 | C2 | semidirect |
| 6. #11720233 | C2 | semidirect |
| 7. #11720230 | C2 | semidirect |
| 13. #88521 | C22 | semidirect |
| 15. C9×D24 | C22 | semidirect |
| 19. C3⋊(C9⋊C16) | C22 | semidirect |
| 20. C9×C3⋊C16 | C22 | semidirect |
| 29. D8×D9 | D3 | semidirect |
| 93. #826 | D9 | semidirect |
| 145. D24 | C2×D9 | semidirect |
| 152. C3⋊C16 | C2×D9 | semidirect |
| 179. C3×C9 | #509 | semidirect |
| 249. C9 | #5147 | semidirect |
| 282. C3 | #10588591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D8×D9 | 2 |
| #11720822 | 2 |
| #11720564 | 2 |
| C9×#826 | 2 |
| #11720238 | 2 |
| #11720233 | 2 |
| #11720230 | 2 |
| #10591031 | 3 |
| #10588591 | 3 |