Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19152308 | C2 | semidirect |
| 3. #19151945 | C2 | semidirect |
| 4. #19151913 | C2 | semidirect |
| 5. #19151893 | C2 | semidirect |
| 6. #19151847 | C2 | semidirect |
| 7. #19151798 | C2 | semidirect |
| 8. #19151759 | C2 | semidirect |
| 9. #19151677 | C2 | semidirect |
| 10. #19151598 | C2 | semidirect |
| 11. C4×Q16×C89 | C2 | semidirect |
| 129. C89 | #3333 | semidirect |
| 138. C4×Q16 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152308 | 2 |
| #19152270 | 2 |
| #19151945 | 2 |
| #19151913 | 2 |
| #19151893 | 2 |
| #19151847 | 2 |
| #19151798 | 2 |
| #19151759 | 2 |
| #19151677 | 2 |
| #19151598 | 2 |
| C4×Q16×C89 | 2 |
| #3333 | 89 |