Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×D89 | C2 | semidirect |
| 2. C2×#15668042 | C2 | semidirect |
| 4. #19151752 | C2 | semidirect |
| 5. #19151735 | C2 | semidirect |
| 6. #19151608 | C2 | semidirect |
| 7. #19151607 | C2 | semidirect |
| 8. #19151561 | C2 | semidirect |
| 9. C2×#137×C89 | C2 | semidirect |
| 19. C2×#13083564 | C22 | semidirect |
| 20. C2×#13083562 | C22 | semidirect |
| 28. #15667937 | C22 | semidirect |
| 29. #15667936 | C22 | semidirect |
| 34. C2×Q16×C89 | C22 | semidirect |
| 35. C2×SD16×C89 | C22 | semidirect |
| 42. C2×Dic178 | D4 | semidirect |
| 70. C2×Q8×C89 | D4 | semidirect |
| 127. C2×D89 | #137 | semidirect |
| 142. C89 | #3004 | semidirect |
| 145. C2×#137 | D89 | semidirect |
| 165. C2×Q16 | C2×D89 | semidirect |
| 167. C2×SD16 | C2×D89 | semidirect |
| 193. C2×Q8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D89 | 2 |
| C2×#15668042 | 2 |
| #19152105 | 2 |
| #19151752 | 2 |
| #19151735 | 2 |
| #19151608 | 2 |
| #19151607 | 2 |
| #19151561 | 2 |
| C2×#137×C89 | 2 |
| #3004 | 89 |