Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×Q8×D89 | C2 | semidirect |
| 2. C2×#15668045 | C2 | semidirect |
| 3. C2×#15668043 | C2 | semidirect |
| 5. #19151755 | C2 | semidirect |
| 6. #19151738 | C2 | semidirect |
| 7. #19151606 | C2 | semidirect |
| 8. #19151561 | C2 | semidirect |
| 9. #419×C89 | C2 | semidirect |
| 21. C2×Dic356 | C22 | semidirect |
| 22. C2×#13083564 | C22 | semidirect |
| 23. C2×#13083563 | C22 | semidirect |
| 24. C2×#13083561 | C22 | semidirect |
| 31. #15667935 | C22 | semidirect |
| 36. #103×C89 | C22 | semidirect |
| 44. C2×Dic178 | D4 | semidirect |
| 73. C2×Q8×C89 | D4 | semidirect |
| 127. C2×D89 | #137 | semidirect |
| 142. C89 | #3004 | semidirect |
| 150. #419 | D89 | semidirect |
| 177. #103 | C2×D89 | semidirect |
| 194. C2×Q8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D89 | 2 |
| C2×#15668045 | 2 |
| C2×#15668043 | 2 |
| #19152110 | 2 |
| #19151755 | 2 |
| #19151738 | 2 |
| #19151606 | 2 |
| #19151561 | 2 |
| #419×C89 | 2 |
| #3004 | 89 |