Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
604 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C3×M16×D9 | C2 | semidirect |
| 3. D9×#208 | C2 | semidirect |
| 4. #11720557 | C2 | semidirect |
| 5. C9×#823 | C2 | semidirect |
| 6. #11720296 | C2 | semidirect |
| 7. #11720288 | C2 | semidirect |
| 19. C3×C9×M16 | C22 | semidirect |
| 20. #88532 | C22 | semidirect |
| 21. C9×#208 | C22 | semidirect |
| 22. C3×#3667 | C22 | semidirect |
| 36. M16×D9 | D3 | semidirect |
| 95. C9×M16 | C2×D3 | semidirect |
| 98. #3667 | C2×D3 | semidirect |
| 131. #823 | D9 | direct (N × H) |
| 188. C3×D9 | #100 | semidirect |
| 212. C3×M16 | C2×D9 | semidirect |
| 220. #208 | C2×D9 | semidirect |
| 266. C3×C9 | C2×#100 | semidirect |
| 331. D9 | #823 | direct (N × H) |
| 346. M16 | D3×D9 | semidirect |
| 384. C9 | C2×#823 | semidirect |
| 437. C3 | D9×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×D12 | 2 |
| C3×M16×D9 | 2 |
| D9×#208 | 2 |
| #11720557 | 2 |
| C9×#823 | 2 |
| #11720296 | 2 |
| #11720288 | 2 |
| D3×#823 | 3 |
| D9×#100 | 3 |