Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19152253 | C2 | semidirect |
| 2. D4×D356 | C2 | semidirect |
| 3. #19151945 | C2 | semidirect |
| 4. #19151913 | C2 | semidirect |
| 5. #19151878 | C2 | semidirect |
| 6. #19151833 | C2 | semidirect |
| 7. #19151793 | C2 | semidirect |
| 8. #19151730 | C2 | semidirect |
| 9. C8×D356 | C2 | semidirect |
| 10. #102×D89 | C2 | semidirect |
| 11. C4×D8×C89 | C2 | semidirect |
| 15. C2×#13083559 | C22 | semidirect |
| 16. C2×C8×D89 | C22 | semidirect |
| 17. #15668012 | C22 | semidirect |
| 23. #15667983 | C22 | semidirect |
| 26. C4⋊C4×D89 | C22 | semidirect |
| 27. #15667945 | C22 | semidirect |
| 28. C4⋊#10623494 | C22 | semidirect |
| 29. #15667934 | C22 | semidirect |
| 30. #15667934 | C22 | semidirect |
| 32. #15667932 | C22 | semidirect |
| 33. #15667924 | C22 | semidirect |
| 36. C4×D4×C89 | C22 | semidirect |
| 37. #107×C89 | C22 | semidirect |
| 39. #102×C89 | C22 | semidirect |
| 40. C4×C8×C89 | C22 | semidirect |
| 88. D4×C89 | #41 | semidirect |
| 105. D356 | D8 | semidirect |
| 143. C89 | #3294 | semidirect |
| 152. C4×D8 | D89 | semidirect |
| 171. C4×D4 | C2×D89 | semidirect |
| 174. #107 | C2×D89 | semidirect |
| 181. #102 | C2×D89 | semidirect |
| 183. C4×C8 | C2×D89 | semidirect |
| 240. D4 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152253 | 2 |
| D4×D356 | 2 |
| #19151945 | 2 |
| #19151913 | 2 |
| #19151878 | 2 |
| #19151833 | 2 |
| #19151793 | 2 |
| #19151730 | 2 |
| C8×D356 | 2 |
| #102×D89 | 2 |
| C4×D8×C89 | 2 |
| #3294 | 89 |