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×#15668034 | C2 | semidirect |
| 2. #19152109 | C2 | semidirect |
| 3. #19151856 | C2 | semidirect |
| 4. #19151851 | C2 | semidirect |
| 5. #19151844 | C2 | semidirect |
| 6. #19151636 | C2 | semidirect |
| 7. #19151595 | C2 | semidirect |
| 8. C22×M16×C89 | C2 | semidirect |
| 11. C2×Dic356 | C22 | semidirect |
| 12. C2×#13083563 | C22 | semidirect |
| 13. C2×D712 | C22 | semidirect |
| 20. #15667946 | C22 | semidirect |
| 21. #15667944 | C22 | semidirect |
| 22. #15667937 | C22 | semidirect |
| 23. #15667934 | C22 | semidirect |
| 56. C2×C8×C89 | D4 | semidirect |
| 106. C89 | #3054 | semidirect |
| 108. C22×M16 | D89 | semidirect |
| 156. C2×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668034 | 2 |
| #19152109 | 2 |
| #19151856 | 2 |
| #19151851 | 2 |
| #19151844 | 2 |
| #19151636 | 2 |
| #19151595 | 2 |
| C22×M16×C89 | 2 |
| #3054 | 89 |