Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19152233 | C2 | semidirect |
| 3. #19151944 | C2 | semidirect |
| 4. #19151910 | C2 | semidirect |
| 5. #19151879 | C2 | semidirect |
| 6. #19151831 | C2 | semidirect |
| 7. #19151730 | C2 | semidirect |
| 8. C4×#13083559 | C2 | semidirect |
| 9. #19151663 | C2 | semidirect |
| 10. #102×D89 | C2 | semidirect |
| 11. #459×C89 | C2 | semidirect |
| 16. C2×C8×D89 | C22 | semidirect |
| 17. #15668012 | C22 | semidirect |
| 22. #15667983 | C22 | semidirect |
| 26. C4⋊C4×D89 | C22 | semidirect |
| 27. #15667946 | C22 | semidirect |
| 28. #15667945 | C22 | semidirect |
| 30. #15667933 | C22 | semidirect |
| 31. #15667933 | C22 | semidirect |
| 32. #15667933 | C22 | semidirect |
| 34. #15667924 | C22 | semidirect |
| 35. C4×#10623494 | C22 | semidirect |
| 36. C2×D8×C89 | C22 | semidirect |
| 38. C4×D4×C89 | C22 | semidirect |
| 39. C4⋊C8×C89 | C22 | semidirect |
| 40. #102×C89 | C22 | semidirect |
| 103. D356 | D8 | semidirect |
| 104. D356 | #41 | semidirect |
| 143. C89 | #3294 | semidirect |
| 150. #459 | D89 | semidirect |
| 159. C2×D8 | C2×D89 | semidirect |
| 171. C4×D4 | C2×D89 | semidirect |
| 175. C4⋊C8 | C2×D89 | semidirect |
| 181. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152253 | 2 |
| #19152233 | 2 |
| #19151944 | 2 |
| #19151910 | 2 |
| #19151879 | 2 |
| #19151831 | 2 |
| #19151730 | 2 |
| C4×#13083559 | 2 |
| #19151663 | 2 |
| #102×D89 | 2 |
| #459×C89 | 2 |
| #3294 | 89 |