Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #19143190 | C2 | semidirect |
| 3. #19136332 | C2 | semidirect |
| 4. C2×#14582710 | C2 | semidirect |
| 5. C43×#3407 | C2 | semidirect |
| 7. #14583716 | C4 | semidirect |
| 9. #14583704 | C4 | semidirect |
| 14. #14582937 | C22 | semidirect |
| 15. C2×#13063257 | C22 | semidirect |
| 16. #14582710 | C22 | semidirect |
| 17. #14582710 | C22 | semidirect |
| 20. C2×M32×C43 | C22 | semidirect |
| 31. #13063347 | C2×C4 | semidirect |
| 33. C2×Dic172 | C2×C4 | semidirect |
| 35. C2×D344 | C2×C4 | semidirect |
| 123. #3407 | D43 | semidirect |
| 140. C2×M32 | C2×D43 | semidirect |
| 146. C43 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149369 | 2 |
| #19143190 | 2 |
| #19136332 | 2 |
| C2×#14582710 | 2 |
| C43×#3407 | 2 |
| #33388 | 43 |