Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13083557 | C2 | semidirect |
| 2. #19152105 | C2 | semidirect |
| 3. #19151853 | C2 | semidirect |
| 4. #19151848 | C2 | semidirect |
| 5. #19151841 | C2 | semidirect |
| 6. #19151636 | C2 | semidirect |
| 7. #19151594 | C2 | semidirect |
| 8. C2×#135×C89 | C2 | semidirect |
| 20. #15667946 | C22 | semidirect |
| 21. #15667944 | C22 | semidirect |
| 22. #15667936 | C22 | semidirect |
| 23. #15667933 | C22 | semidirect |
| 26. C2×Q16×C89 | C22 | semidirect |
| 27. C2×SD16×C89 | C22 | semidirect |
| 28. C2×D8×C89 | C22 | semidirect |
| 57. C2×C8×C89 | D4 | semidirect |
| 106. C89 | #3054 | semidirect |
| 107. C2×#135 | D89 | semidirect |
| 118. C2×Q16 | C2×D89 | semidirect |
| 119. C2×SD16 | C2×D89 | semidirect |
| 120. C2×D8 | C2×D89 | semidirect |
| 157. C2×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083557 | 2 |
| #19152105 | 2 |
| #19151853 | 2 |
| #19151848 | 2 |
| #19151841 | 2 |
| #19151636 | 2 |
| #19151594 | 2 |
| C2×#135×C89 | 2 |
| #3054 | 89 |