Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×Q16×D89 | C2 | semidirect |
| 4. #19151857 | C2 | semidirect |
| 5. #19151856 | C2 | semidirect |
| 6. #19151855 | C2 | semidirect |
| 7. #19151854 | C2 | semidirect |
| 8. #19151853 | C2 | semidirect |
| 9. #106×D89 | C2 | semidirect |
| 10. #103×D89 | C2 | semidirect |
| 11. #470×C89 | C2 | semidirect |
| 14. C2×Dic356 | C22 | semidirect |
| 15. C2×#13083564 | C22 | semidirect |
| 31. #15667944 | C22 | semidirect |
| 32. #15667943 | C22 | semidirect |
| 33. #15667937 | C22 | semidirect |
| 34. #15667936 | C22 | semidirect |
| 35. #15667935 | C22 | semidirect |
| 36. C2×Q16×C89 | C22 | semidirect |
| 39. #106×C89 | C22 | semidirect |
| 40. #103×C89 | C22 | semidirect |
| 135. D89 | #470 | direct (N × H) |
| 137. C89 | C2×#470 | semidirect |
| 146. #470 | D89 | direct (N × H) |
| 154. C2×Q16 | C2×D89 | semidirect |
| 173. #106 | C2×D89 | semidirect |
| 177. #103 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D89 | 2 |
| C2×M16×D89 | 2 |
| C22⋊Q8×D89 | 2 |
| #19151857 | 2 |
| #19151856 | 2 |
| #19151855 | 2 |
| #19151854 | 2 |
| #19151853 | 2 |
| #106×D89 | 2 |
| #103×D89 | 2 |
| #470×C89 | 2 |
| C2×#470 | 89 |