Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #19152434 | C2 | semidirect |
| 2. C2×#15668040 | C2 | semidirect |
| 3. #19152162 | C2 | semidirect |
| 4. #19151773 | C2 | semidirect |
| 5. #19151768 | C2 | semidirect |
| 6. #19151614 | C2 | semidirect |
| 7. #413×C89 | C2 | semidirect |
| 8. #15668060 | C22 | semidirect |
| 12. #15668057 | C22 | semidirect |
| 16. C22×D356 | C22 | semidirect |
| 18. #15668040 | C22 | semidirect |
| 21. #15668008 | C22 | semidirect |
| 22. #15668001 | C22 | semidirect |
| 25. #15667971 | C22 | semidirect |
| 26. #15667938 | C22 | semidirect |
| 28. C2×M16×C89 | C22 | semidirect |
| 29. #101×C89 | C22 | semidirect |
| 30. #100×C89 | C22 | semidirect |
| 38. #13083574 | D4 | semidirect |
| 43. C2×Dic178 | D4 | semidirect |
| 49. C2×D356 | D4 | semidirect |
| 135. C89 | #3021 | semidirect |
| 142. #413 | D89 | semidirect |
| 157. C2×M16 | C2×D89 | semidirect |
| 164. #101 | C2×D89 | semidirect |
| 165. #100 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152434 | 2 |
| C2×#15668040 | 2 |
| #19152162 | 2 |
| #19151773 | 2 |
| #19151768 | 2 |
| #19151614 | 2 |
| #413×C89 | 2 |
| #3021 | 89 |