Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152415 | C2 | semidirect |
| 2. #19152408 | C2 | semidirect |
| 3. #19152399 | C2 | semidirect |
| 4. #19151981 | C2 | semidirect |
| 5. #19151874 | C2 | semidirect |
| 6. #19151860 | C2 | semidirect |
| 7. #19151778 | C2 | semidirect |
| 8. #19151769 | C2 | semidirect |
| 9. #19151714 | C2 | semidirect |
| 10. #19151713 | C2 | semidirect |
| 11. #472×C89 | C2 | semidirect |
| 12. #15668059 | C22 | semidirect |
| 16. #15668045 | C22 | semidirect |
| 27. C2×Dic356 | C22 | semidirect |
| 28. C2×#13083562 | C22 | semidirect |
| 31. #15668020 | C22 | semidirect |
| 33. #15667999 | C22 | semidirect |
| 34. #15667947 | C22 | semidirect |
| 35. #15667939 | C22 | semidirect |
| 37. #15667938 | C22 | semidirect |
| 38. #15667930 | C22 | semidirect |
| 39. C8×Dic89 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C89 | C22 | semidirect |
| 42. #131×C89 | C22 | semidirect |
| 43. #108×C89 | C22 | semidirect |
| 44. #100×C89 | C22 | semidirect |
| 150. C89 | #3290 | semidirect |
| 156. #472 | D89 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D89 | semidirect |
| 185. #131 | C2×D89 | semidirect |
| 188. #108 | C2×D89 | semidirect |
| 193. #100 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152415 | 2 |
| #19152408 | 2 |
| #19152399 | 2 |
| #19151981 | 2 |
| #19151874 | 2 |
| #19151860 | 2 |
| #19151778 | 2 |
| #19151769 | 2 |
| #19151714 | 2 |
| #19151713 | 2 |
| #472×C89 | 2 |
| #3290 | 89 |