Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15668042 | C2 | semidirect |
| 3. C2×#15668000 | C2 | semidirect |
| 4. #19151820 | C2 | semidirect |
| 5. #19151813 | C2 | semidirect |
| 6. #19151622 | C2 | semidirect |
| 7. #19151606 | C2 | semidirect |
| 8. #19151602 | C2 | semidirect |
| 9. C4×#41×C89 | C2 | semidirect |
| 14. C2×#13083564 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 24. C4⋊#10623494 | C22 | semidirect |
| 25. #15667935 | C22 | semidirect |
| 28. C4×Q8×C89 | C22 | semidirect |
| 30. C4×D4×C89 | C22 | semidirect |
| 126. C89 | #3040 | semidirect |
| 130. C4×#41 | D89 | semidirect |
| 150. C4×Q8 | C2×D89 | semidirect |
| 152. C4×D4 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668042 | 2 |
| C2×#15668037 | 2 |
| C2×#15668000 | 2 |
| #19151820 | 2 |
| #19151813 | 2 |
| #19151622 | 2 |
| #19151606 | 2 |
| #19151602 | 2 |
| C4×#41×C89 | 2 |
| #3040 | 89 |