Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
452 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11757416 | C2 | direct (N × H) |
| 3. C23×C32⋊C9 | C3 | semidirect |
| 4. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 9. C22×C32⋊C9 | C2×C3 | semidirect |
| 10. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 17. C2×C32×A4 | C9 | semidirect |
| 24. C2×C32⋊C9 | A4 | semidirect |
| 32. C32×A4 | C2×C9 | semidirect |
| 39. C32⋊C9 | C2×A4 | semidirect |
| 154. C23 | #6866 | semidirect |
| 173. C22 | C2×#6866 | semidirect |
| 182. C2 | #11757416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757416 | 2 |
| C2×C33×A4 | 3 |
| C23×C32⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×#6866 | 4 |