Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#15668000 | C2 | semidirect |
| 2. #19151980 | C2 | semidirect |
| 3. #19151955 | C2 | semidirect |
| 4. #19151820 | C2 | semidirect |
| 5. #19151813 | C2 | semidirect |
| 6. #19151753 | C2 | semidirect |
| 7. #19151748 | C2 | semidirect |
| 8. #19151736 | C2 | semidirect |
| 10. #19151651 | C2 | semidirect |
| 11. #529×C89 | C2 | semidirect |
| 14. C2×#13083564 | C22 | semidirect |
| 15. C2×#13083562 | C22 | semidirect |
| 24. C4⋊#10623494 | C22 | semidirect |
| 25. #15667935 | C22 | semidirect |
| 26. #15667935 | C22 | semidirect |
| 31. C4×#10623494 | C22 | semidirect |
| 33. #125×C89 | C22 | semidirect |
| 34. #124×C89 | C22 | semidirect |
| 38. C4×Q8×C89 | C22 | semidirect |
| 40. C4×D4×C89 | C22 | semidirect |
| 144. C89 | #3211 | semidirect |
| 145. #529 | D89 | semidirect |
| 163. #125 | C2×D89 | semidirect |
| 168. #124 | C2×D89 | semidirect |
| 172. C4×Q8 | C2×D89 | semidirect |
| 174. 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×#15668000 | 2 |
| #19151980 | 2 |
| #19151955 | 2 |
| #19151820 | 2 |
| #19151813 | 2 |
| #19151753 | 2 |
| #19151748 | 2 |
| #19151736 | 2 |
| #19151731 | 2 |
| #19151651 | 2 |
| #529×C89 | 2 |
| #3211 | 89 |