Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#14582937 | C2 | semidirect |
| 3. #19136804 | C2 | semidirect |
| 4. #19136787 | C2 | semidirect |
| 5. #19136383 | C2 | semidirect |
| 6. #19136308 | C2 | semidirect |
| 7. C43×#2112 | C2 | semidirect |
| 20. #14582727 | C22 | semidirect |
| 21. #14582725 | C22 | semidirect |
| 22. #14582704 | C22 | semidirect |
| 23. #14582701 | C22 | semidirect |
| 145. #2112 | D43 | semidirect |
| 170. C43 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144176 | 2 |
| C2×#14582937 | 2 |
| #19136804 | 2 |
| #19136787 | 2 |
| #19136383 | 2 |
| #19136308 | 2 |
| C43×#2112 | 2 |
| #33647 | 43 |