Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152321 | C2 | semidirect |
| 3. #19151945 | C2 | semidirect |
| 4. #19151924 | C2 | semidirect |
| 5. #19151878 | C2 | semidirect |
| 6. #19151847 | C2 | semidirect |
| 7. #19151798 | C2 | semidirect |
| 8. #19151747 | C2 | semidirect |
| 9. #19151677 | C2 | semidirect |
| 10. #19151601 | C2 | semidirect |
| 11. C4×SD16×C89 | C2 | semidirect |
| 14. C2×#13083561 | C22 | semidirect |
| 15. C2×#13083557 | C22 | semidirect |
| 16. #15668012 | C22 | semidirect |
| 20. #15667988 | C22 | semidirect |
| 26. #15667970 | 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 |
| 35. C4×Q8×C89 | C22 | semidirect |
| 37. #106×C89 | C22 | semidirect |
| 38. #103×C89 | C22 | semidirect |
| 40. C4×C8×C89 | C22 | semidirect |
| 136. C89 | #3324 | semidirect |
| 145. C4×SD16 | D89 | semidirect |
| 162. C4×Q8 | C2×D89 | semidirect |
| 167. #106 | C2×D89 | semidirect |
| 169. #103 | C2×D89 | semidirect |
| 176. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152321 | 2 |
| D4×D356 | 2 |
| #19151945 | 2 |
| #19151924 | 2 |
| #19151878 | 2 |
| #19151847 | 2 |
| #19151798 | 2 |
| #19151747 | 2 |
| #19151677 | 2 |
| #19151601 | 2 |
| C4×SD16×C89 | 2 |
| #3324 | 89 |