Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 163 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. #19145978 | C2 | semidirect |
| 3. #19133820 | C2 | semidirect |
| 4. #19133771 | C2 | semidirect |
| 5. #19133330 | C2 | semidirect |
| 6. #19133047 | C2 | semidirect |
| 7. C43×#3131 | C2 | semidirect |
| 17. #14583176 | C22 | semidirect |
| 19. #14583101 | C22 | semidirect |
| 21. #14582923 | C22 | semidirect |
| 22. #14582648 | C22 | semidirect |
| 24. #14582628 | C22 | semidirect |
| 25. C43×#533 | C22 | semidirect |
| 28. C43×#487 | C22 | semidirect |
| 31. C2×C4×C8×C43 | C22 | semidirect |
| 177. #3131 | D43 | semidirect |
| 194. #533 | C2×D43 | semidirect |
| 198. #487 | C2×D43 | semidirect |
| 207. C2×C4×C8 | C2×D43 | semidirect |
| 211. C43 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149000 | 2 |
| #19145978 | 2 |
| #19133820 | 2 |
| #19133771 | 2 |
| #19133330 | 2 |
| #19133047 | 2 |
| C43×#3131 | 2 |
| #18691 | 43 |