Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19136912 | C2 | semidirect |
| 2. C2×#14582737 | C2 | semidirect |
| 3. #19136720 | C2 | semidirect |
| 4. #19132785 | C2 | semidirect |
| 5. #19132779 | C2 | semidirect |
| 6. #19132737 | C2 | semidirect |
| 8. C2×Dic344 | C22 | semidirect |
| 13. #14582733 | C22 | semidirect |
| 14. C2×C43⋊C32 | C22 | semidirect |
| 15. #14582729 | C22 | semidirect |
| 144. C43 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136912 | 2 |
| C2×#14582737 | 2 |
| #19136720 | 2 |
| #19132785 | 2 |
| #19132779 | 2 |
| #19132737 | 2 |
| C43×#3415 | 2 |
| #13671 | 43 |