Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
148 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 28 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. #11757435 | C2 | direct (N × H) |
| 2. C23×#732 | C3 | semidirect |
| 3. C2×#66359 | C3 | semidirect |
| 4. C2×#66358 | C3 | semidirect |
| 5. C2×C9⋊(C22⋊C9) | C3 | semidirect |
| 9. C22×#732 | C2×C3 | semidirect |
| 10. #66359 | C2×C3 | semidirect |
| 11. #66358 | C2×C3 | semidirect |
| 12. C9⋊(C22⋊C9) | C2×C3 | semidirect |
| 23. C2×#732 | A4 | semidirect |
| 36. #732 | C2×A4 | semidirect |
| 102. C23 | #6881 | semidirect |
| 115. C22 | C2×#6881 | semidirect |
| 122. C2 | #11757435 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757435 | 2 |
| C23×#732 | 3 |
| C2×#66359 | 3 |
| C2×#66358 | 3 |
| C2×C9⋊(C22⋊C9) | 3 |
| C2×#6881 | 4 |