Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #19143446 | C2 | semidirect |
| 3. #19136470 | C2 | semidirect |
| 4. #19136441 | C2 | semidirect |
| 5. #19136310 | C2 | semidirect |
| 6. #19136191 | C2 | semidirect |
| 7. C43×#2158 | C2 | semidirect |
| 10. C2×D688 | C4 | semidirect |
| 15. #14582981 | C22 | semidirect |
| 18. #14582699 | C22 | semidirect |
| 19. #14582674 | C22 | semidirect |
| 20. C16×Dic43 | C22 | semidirect |
| 23. C43×#367 | C22 | semidirect |
| 24. C43×#366 | C22 | semidirect |
| 28. C2×D344 | C2×C4 | semidirect |
| 35. D688 | C2×C4 | semidirect |
| 36. D688 | C2×C4 | semidirect |
| 44. C2×C16×C43 | C2×C4 | semidirect |
| 109. #2158 | D43 | semidirect |
| 128. #367 | C2×D43 | semidirect |
| 129. #366 | C2×D43 | semidirect |
| 133. C43 | #33456 | semidirect |
| 150. C2×C16 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D688 | 2 |
| #19143446 | 2 |
| #19136470 | 2 |
| #19136441 | 2 |
| #19136310 | 2 |
| #19136191 | 2 |
| C43×#2158 | 2 |
| #33456 | 43 |