Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #19152000 | C2 | semidirect |
| 3. #19151937 | C2 | semidirect |
| 4. #19151927 | C2 | semidirect |
| 5. #19151905 | C2 | semidirect |
| 6. #19151836 | C2 | semidirect |
| 7. #19151836 | C2 | semidirect |
| 9. #19151635 | C2 | semidirect |
| 10. #107×D89 | C2 | semidirect |
| 11. C4×Q16×C89 | C2 | semidirect |
| 115. C89 | #3336 | semidirect |
| 123. C4×Q16 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152289 | 2 |
| #19152000 | 2 |
| #19151937 | 2 |
| #19151927 | 2 |
| #19151905 | 2 |
| #19151836 | 2 |
| C8×D356 | 2 |
| #19151635 | 2 |
| #107×D89 | 2 |
| C4×Q16×C89 | 2 |
| #3336 | 89 |