Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#15667971 | C2 | semidirect |
| 3. #19151923 | C2 | semidirect |
| 4. #19151917 | C2 | semidirect |
| 5. #19151912 | C2 | semidirect |
| 6. #19151640 | C2 | semidirect |
| 7. #19151604 | C2 | semidirect |
| 8. #407×C89 | C2 | semidirect |
| 18. #15667971 | C22 | semidirect |
| 20. C2×C4⋊Dic89 | C22 | semidirect |
| 21. C2×C4⋊Dic89 | C22 | semidirect |
| 25. #15667946 | C22 | semidirect |
| 26. #15667944 | C22 | semidirect |
| 27. #15667934 | C22 | semidirect |
| 28. #15667934 | C22 | semidirect |
| 31. C22⋊C8×C89 | C22 | semidirect |
| 32. C22⋊C8×C89 | C22 | semidirect |
| 126. C89 | #3094 | semidirect |
| 134. #407 | D89 | semidirect |
| 157. C22⋊C8 | C2×D89 | semidirect |
| 158. C22⋊C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667986 | 2 |
| C2×#15667971 | 2 |
| #19151923 | 2 |
| #19151917 | 2 |
| #19151912 | 2 |
| #19151640 | 2 |
| #19151604 | 2 |
| #407×C89 | 2 |
| #3094 | 89 |