Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19145334 | C2 | semidirect |
| 2. #19143500 | C2 | semidirect |
| 3. #19136811 | C2 | semidirect |
| 4. #19136763 | C2 | semidirect |
| 5. #19136672 | C2 | semidirect |
| 6. #19136671 | C2 | semidirect |
| 7. #19136542 | C2 | semidirect |
| 8. #19136492 | C2 | semidirect |
| 9. #19136490 | C2 | semidirect |
| 10. #19136406 | C2 | semidirect |
| 11. C43×#2230 | C2 | semidirect |
| 17. #14583276 | C22 | semidirect |
| 27. #14583010 | C22 | semidirect |
| 31. #14582721 | C22 | semidirect |
| 32. #14582720 | C22 | semidirect |
| 33. #14582713 | C22 | semidirect |
| 34. #14582711 | C22 | semidirect |
| 37. #14582676 | C22 | semidirect |
| 38. C43×#498 | C22 | semidirect |
| 40. C43×#365 | C22 | semidirect |
| 41. C43×#364 | C22 | semidirect |
| 113. Q16×C43 | #41 | semidirect |
| 115. D8×C43 | #41 | semidirect |
| 137. Dic172 | #41 | semidirect |
| 142. D344 | #41 | semidirect |
| 219. #2230 | D43 | semidirect |
| 237. #498 | C2×D43 | semidirect |
| 254. #365 | C2×D43 | semidirect |
| 256. #364 | C2×D43 | semidirect |
| 263. C43 | #33688 | semidirect |
| 336. Q16 | #10621902 | semidirect |
| 347. D8 | #10621902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145334 | 2 |
| #19143500 | 2 |
| #19136811 | 2 |
| #19136763 | 2 |
| #19136672 | 2 |
| #19136671 | 2 |
| #19136542 | 2 |
| #19136492 | 2 |
| #19136490 | 2 |
| #19136406 | 2 |
| C43×#2230 | 2 |
| #33688 | 43 |