Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #19136809 | C2 | semidirect |
| 3. #19136369 | C2 | semidirect |
| 4. C2×#14582711 | C2 | semidirect |
| 5. #19136216 | C2 | semidirect |
| 6. C43×#2916 | C2 | semidirect |
| 14. #14582723 | C22 | semidirect |
| 16. #14582681 | C22 | semidirect |
| 20. C43×#430 | C22 | semidirect |
| 127. #2916 | D43 | semidirect |
| 145. #430 | C2×D43 | semidirect |
| 153. C43 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144243 | 2 |
| #19136809 | 2 |
| #19136369 | 2 |
| C2×#14582711 | 2 |
| #19136216 | 2 |
| C43×#2916 | 2 |
| #33657 | 43 |