Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #19137197 | C2 | semidirect |
| 5. C2×#14582624 | C2 | semidirect |
| 6. #19132462 | C2 | semidirect |
| 7. C43×#1289 | C2 | semidirect |
| 12. #14582831 | C4 | semidirect |
| 14. #14582817 | C4 | semidirect |
| 220. #1289 | D43 | semidirect |
| 250. C43 | #9206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19140340 | 2 |
| #19137197 | 2 |
| #19133164 | 2 |
| #19133162 | 2 |
| C2×#14582624 | 2 |
| #19132462 | 2 |
| C43×#1289 | 2 |
| #9206 | 43 |