Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 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. C2×#15668038 | C2 | semidirect |
| 2. #19152148 | C2 | semidirect |
| 3. #19151813 | C2 | semidirect |
| 4. #19151803 | C2 | semidirect |
| 5. #19151793 | C2 | semidirect |
| 6. #19151622 | C2 | semidirect |
| 7. #19151597 | C2 | semidirect |
| 8. C2×C4×D4×C89 | C2 | semidirect |
| 14. #15668012 | C22 | semidirect |
| 15. #15668009 | C22 | semidirect |
| 16. #15668000 | C22 | semidirect |
| 21. C4⋊#10623494 | C22 | semidirect |
| 22. C4⋊#10623494 | C22 | semidirect |
| 23. #15667935 | C22 | semidirect |
| 24. #15667932 | C22 | semidirect |
| 53. C2×D4×C89 | D4 | semidirect |
| 119. C4×C89 | AGL(1,ℤ/8) | semidirect |
| 130. C89 | #3036 | semidirect |
| 133. C2×C4×D4 | D89 | semidirect |
| 174. C2×D4 | D356 | semidirect |
| 250. C4 | #15668038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668038 | 2 |
| #19152148 | 2 |
| #19151813 | 2 |
| #19151803 | 2 |
| #19151793 | 2 |
| #19151622 | 2 |
| #19151597 | 2 |
| C2×C4×D4×C89 | 2 |
| #3036 | 89 |