Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 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 |
|---|---|---|
| 2. C22×#13083561 | C2 | semidirect |
| 3. #19152172 | C2 | semidirect |
| 4. #19151759 | C2 | semidirect |
| 5. #19151747 | C2 | semidirect |
| 6. #19151604 | C2 | semidirect |
| 7. #19151594 | C2 | semidirect |
| 8. #19151566 | C2 | semidirect |
| 9. C2×#137×C89 | C2 | semidirect |
| 20. C2×#13083561 | C22 | semidirect |
| 21. C22×#10623494 | C22 | semidirect |
| 25. #15667988 | C22 | semidirect |
| 26. #15667971 | C22 | semidirect |
| 27. #15667936 | C22 | semidirect |
| 28. #15667934 | C22 | semidirect |
| 29. #15667933 | C22 | semidirect |
| 30. #15667924 | C22 | semidirect |
| 32. C22×Q8×C89 | C22 | semidirect |
| 34. C2×Q16×C89 | C22 | semidirect |
| 35. C2×SD16×C89 | C22 | semidirect |
| 36. C2×M16×C89 | C22 | semidirect |
| 147. C89 | #3009 | semidirect |
| 149. C2×#137 | D89 | semidirect |
| 163. C22×Q8 | C2×D89 | semidirect |
| 169. C2×Q16 | C2×D89 | semidirect |
| 172. C2×SD16 | C2×D89 | semidirect |
| 173. C2×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668058 | 2 |
| C22×#13083561 | 2 |
| #19152172 | 2 |
| #19151759 | 2 |
| #19151747 | 2 |
| #19151604 | 2 |
| #19151594 | 2 |
| #19151566 | 2 |
| C2×#137×C89 | 2 |
| #3009 | 89 |