Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #19152033 | C2 | semidirect |
| 2. C2×#15667953 | C2 | semidirect |
| 3. #19151868 | C2 | semidirect |
| 4. #19151411 | C2 | semidirect |
| 5. #19151405 | C2 | semidirect |
| 6. #19151382 | C2 | semidirect |
| 7. #576×C89 | C2 | semidirect |
| 9. C2×D712 | C22 | semidirect |
| 13. #15667952 | C22 | semidirect |
| 14. C2×#13083549 | C22 | semidirect |
| 15. #15667948 | C22 | semidirect |
| 94. C89 | #2192 | semidirect |
| 95. #576 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152033 | 2 |
| C2×#15667953 | 2 |
| #19151868 | 2 |
| #19151411 | 2 |
| #19151405 | 2 |
| #19151382 | 2 |
| #576×C89 | 2 |
| #2192 | 89 |