Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #19145333 | C2 | semidirect |
| 2. #19136809 | C2 | semidirect |
| 3. #19136766 | C2 | semidirect |
| 4. #19136671 | C2 | semidirect |
| 5. #19136541 | C2 | semidirect |
| 6. #19136493 | C2 | semidirect |
| 7. #19136407 | C2 | semidirect |
| 8. C43×#2956 | C2 | semidirect |
| 11. #14583297 | C22 | semidirect |
| 12. #14583276 | C22 | semidirect |
| 17. #14583012 | C22 | semidirect |
| 18. #14582723 | C22 | semidirect |
| 19. #14582720 | C22 | semidirect |
| 20. #14582711 | C22 | semidirect |
| 23. #14582677 | C22 | semidirect |
| 89. Q16×C43 | #41 | semidirect |
| 93. D8×C43 | #41 | semidirect |
| 166. #2956 | D43 | semidirect |
| 202. C43 | #33688 | semidirect |
| 259. Q16 | #10621898 | semidirect |
| 265. D8 | #10621898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145333 | 2 |
| #19136809 | 2 |
| #19136766 | 2 |
| #19136671 | 2 |
| #19136541 | 2 |
| #19136493 | 2 |
| #19136407 | 2 |
| C43×#2956 | 2 |
| #33688 | 43 |