Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15668060 | C2 | semidirect |
| 2. #19152396 | C2 | semidirect |
| 3. #19151780 | C2 | semidirect |
| 4. #19151770 | C2 | semidirect |
| 5. #19151616 | C2 | semidirect |
| 6. C2×#15667931 | C2 | semidirect |
| 7. #536×C89 | C2 | semidirect |
| 15. #15668043 | C22 | semidirect |
| 17. #15668038 | C22 | semidirect |
| 21. #15667940 | C22 | semidirect |
| 22. #15667931 | C22 | semidirect |
| 25. C4⋊Q8×C89 | C22 | semidirect |
| 26. #124×C89 | C22 | semidirect |
| 124. C89 | #3020 | semidirect |
| 127. #536 | D89 | semidirect |
| 147. C4⋊Q8 | C2×D89 | semidirect |
| 148. #124 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668060 | 2 |
| #19152396 | 2 |
| #19151780 | 2 |
| #19151770 | 2 |
| #19151616 | 2 |
| C2×#15667931 | 2 |
| #536×C89 | 2 |
| #3020 | 89 |