Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D89 | C2 | semidirect |
| 3. #19151992 | C2 | semidirect |
| 4. #19151990 | C2 | semidirect |
| 5. #19151968 | C2 | semidirect |
| 6. #19151807 | C2 | semidirect |
| 7. #19151802 | C2 | semidirect |
| 8. #19151755 | C2 | semidirect |
| 10. #19151653 | C2 | semidirect |
| 11. #491×C89 | C2 | semidirect |
| 136. C89 | #3218 | semidirect |
| 142. #491 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D89 | 2 |
| #19152133 | 2 |
| #19151992 | 2 |
| #19151990 | 2 |
| #19151968 | 2 |
| #19151807 | 2 |
| #19151802 | 2 |
| #19151755 | 2 |
| #19151738 | 2 |
| #19151653 | 2 |
| #491×C89 | 2 |
| #3218 | 89 |