Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. C2×#15668037 | C2 | semidirect |
| 2. C2×#15668037 | C2 | semidirect |
| 3. #19152365 | C2 | semidirect |
| 4. #19151866 | C2 | semidirect |
| 5. #19151863 | C2 | semidirect |
| 6. #19151646 | C2 | semidirect |
| 7. #19151582 | C2 | semidirect |
| 8. C2×#15667928 | C2 | semidirect |
| 9. #575×C89 | C2 | semidirect |
| 16. C2×#13083561 | C22 | semidirect |
| 18. C2×#13083559 | C22 | semidirect |
| 20. #15668019 | C22 | semidirect |
| 25. #15667947 | C22 | semidirect |
| 26. #15667931 | C22 | semidirect |
| 27. #15667929 | C22 | semidirect |
| 28. #15667928 | C22 | semidirect |
| 32. #137×C89 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C89 | C22 | semidirect |
| 148. C89 | #3068 | semidirect |
| 149. #575 | D89 | semidirect |
| 162. #137 | C2×D89 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668037 | 2 |
| #19152365 | 2 |
| #19151866 | 2 |
| #19151863 | 2 |
| #19151646 | 2 |
| #19151582 | 2 |
| C2×#15667928 | 2 |
| #575×C89 | 2 |
| #3068 | 89 |