Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#15668035 | C2 | semidirect |
| 2. C2×D8×D89 | C2 | semidirect |
| 3. #19152241 | C2 | semidirect |
| 4. #19151836 | C2 | semidirect |
| 5. #19151831 | C2 | semidirect |
| 6. #19151810 | C2 | semidirect |
| 7. #19151747 | C2 | semidirect |
| 8. #19151742 | C2 | semidirect |
| 9. C4×D712 | C2 | semidirect |
| 10. C8×D356 | C2 | semidirect |
| 11. #495×C89 | C2 | semidirect |
| 12. C2×#13083575 | C22 | semidirect |
| 15. C2×#13083561 | C22 | semidirect |
| 20. C2×C8×D89 | C22 | semidirect |
| 24. #15667983 | C22 | semidirect |
| 27. C4×D356 | C22 | semidirect |
| 29. #15667946 | C22 | semidirect |
| 30. C4⋊#10623494 | C22 | semidirect |
| 31. #15667936 | C22 | semidirect |
| 32. #15667934 | C22 | semidirect |
| 33. #15667933 | C22 | semidirect |
| 35. #15667924 | C22 | semidirect |
| 36. C2×Q16×C89 | C22 | semidirect |
| 37. C2×SD16×C89 | C22 | semidirect |
| 39. #124×C89 | C22 | semidirect |
| 40. C4×C8×C89 | C22 | semidirect |
| 56. D712 | D4 | semidirect |
| 127. C2×D89 | #135 | semidirect |
| 144. C89 | #3280 | semidirect |
| 148. #495 | D89 | semidirect |
| 159. C2×Q16 | C2×D89 | semidirect |
| 161. C2×SD16 | C2×D89 | semidirect |
| 168. #124 | C2×D89 | semidirect |
| 184. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668035 | 2 |
| C2×D8×D89 | 2 |
| #19152241 | 2 |
| #19151836 | 2 |
| #19151831 | 2 |
| #19151810 | 2 |
| #19151747 | 2 |
| #19151742 | 2 |
| C4×D712 | 2 |
| C8×D356 | 2 |
| #495×C89 | 2 |
| #3280 | 89 |