Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11757772 | C2 | direct (N × H) |
| 6. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 7. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 8. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 9. C2×(C22⋊C9)⋊C9 | C3 | semidirect |
| 10. C2×C9×C22⋊C9 | C3 | semidirect |
| 18. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 19. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 20. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 21. (C22⋊C9)⋊C9 | C2×C3 | semidirect |
| 22. C9×C22⋊C9 | C2×C3 | semidirect |
| 192. C23 | #6897 | semidirect |
| 210. C22 | C2×#6897 | semidirect |
| 218. C2 | #11757772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757772 | 2 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×(C22⋊C9)⋊C9 | 3 |
| C2×C9×C22⋊C9 | 3 |
| C2×#6897 | 4 |