Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #19143230 | C2 | semidirect |
| 3. #19135441 | C2 | semidirect |
| 4. #19135433 | C2 | semidirect |
| 5. #19134521 | C2 | semidirect |
| 6. #19134516 | C2 | semidirect |
| 7. C43×#1783 | C2 | semidirect |
| 16. #14582922 | C22 | semidirect |
| 17. C2×#13063243 | C22 | semidirect |
| 19. C2×#13063241 | C22 | semidirect |
| 21. M16×Dic43 | C22 | semidirect |
| 159. #1783 | D43 | semidirect |
| 183. C43 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583466 | 2 |
| #19143230 | 2 |
| #19135441 | 2 |
| #19135433 | 2 |
| #19134521 | 2 |
| #19134516 | 2 |
| C43×#1783 | 2 |
| #21801 | 43 |