Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13083573 | C2 | semidirect |
| 2. C2×#15668042 | C2 | semidirect |
| 3. #19152105 | C2 | semidirect |
| 4. #19151757 | C2 | semidirect |
| 5. #19151740 | C2 | semidirect |
| 6. #19151608 | C2 | semidirect |
| 7. #19151603 | C2 | semidirect |
| 8. #19151561 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C89 | C2 | semidirect |
| 19. C2×#13083564 | C22 | semidirect |
| 20. C2×#13083562 | C22 | semidirect |
| 23. #15667988 | C22 | semidirect |
| 24. #15667983 | C22 | semidirect |
| 28. #15667937 | C22 | semidirect |
| 29. #15667933 | C22 | semidirect |
| 30. #15667924 | C22 | semidirect |
| 34. C2×SD16×C89 | C22 | semidirect |
| 35. C2×D8×C89 | C22 | semidirect |
| 43. C2×Dic178 | D4 | semidirect |
| 73. C2×D4×C89 | D4 | semidirect |
| 146. C89 | #3005 | semidirect |
| 149. C2×AGL(1,ℤ/8) | D89 | semidirect |
| 170. C2×SD16 | C2×D89 | semidirect |
| 171. C2×D8 | C2×D89 | semidirect |
| 201. C2×D4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083573 | 2 |
| C2×#15668042 | 2 |
| #19152105 | 2 |
| #19151757 | 2 |
| #19151740 | 2 |
| #19151608 | 2 |
| #19151603 | 2 |
| #19151561 | 2 |
| C2×AGL(1,ℤ/8)×C89 | 2 |
| #3005 | 89 |