Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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. #19142847 | C2 | direct (N × H) |
| 2. C2×#14582812 | C2 | semidirect |
| 3. C2×#14582811 | C2 | semidirect |
| 4. C2×#14582810 | C2 | semidirect |
| 6. C2×C43×#393 | C2 | semidirect |
| 8. C23×Dic86 | C22 | semidirect |
| 12. #14582812 | C22 | semidirect |
| 13. #14582811 | C22 | semidirect |
| 14. #14582810 | C22 | semidirect |
| 16. C2×C43⋊#95 | C22 | semidirect |
| 17. C2×C43⋊#95 | C22 | semidirect |
| 18. C23×Q8×C43 | C22 | semidirect |
| 20. C43×#393 | C22 | semidirect |
| 21. C2×#95×C43 | C22 | semidirect |
| 24. C24×D43 | Q8 | semidirect |
| 29. C22×Dic86 | C23 | semidirect |
| 37. C43⋊#95 | C23 | semidirect |
| 38. C43⋊#95 | C23 | semidirect |
| 41. C22×Q8×C43 | C23 | semidirect |
| 46. #95×C43 | C23 | semidirect |
| 60. C23×D43 | C2×Q8 | semidirect |
| 136. C2×#393 | D43 | semidirect |
| 139. C2×C43 | #2840 | semidirect |
| 146. C23×Q8 | C2×D43 | semidirect |
| 154. #393 | C2×D43 | semidirect |
| 158. C2×#95 | C2×D43 | semidirect |
| 159. C43 | C2×#2840 | semidirect |
| 170. C22×Q8 | C22×D43 | semidirect |
| 184. #95 | C22×D43 | semidirect |
| 271. C2 | #19142847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19142847 | 2 |
| C2×#14582812 | 2 |
| C2×#14582811 | 2 |
| C2×#14582810 | 2 |
| C2×#14582754 | 2 |
| C2×C43×#393 | 2 |
| C2×#2840 | 43 |