Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
140 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 140 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. #11757438 | C2 | direct (N × H) |
| 2. C23×#733 | C3 | semidirect |
| 3. C2×#66359 | C3 | semidirect |
| 5. C2×C9×C22⋊C9 | C3 | semidirect |
| 9. C22×#733 | C2×C3 | semidirect |
| 10. #66359 | C2×C3 | semidirect |
| 12. C9×C22⋊C9 | C2×C3 | semidirect |
| 22. C2×#733 | A4 | semidirect |
| 35. #733 | C2×A4 | semidirect |
| 98. C23 | #6878 | semidirect |
| 108. C22 | C2×#6878 | semidirect |
| 114. C2 | #11757438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757438 | 2 |
| C23×#733 | 3 |
| C2×#66359 | 3 |
| C2×#66358 | 3 |
| C2×C9×C22⋊C9 | 3 |
| C2×#6878 | 4 |