Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #19151949 | C2 | semidirect |
| 4. #19151935 | C2 | semidirect |
| 5. #19151893 | C2 | semidirect |
| 6. #19151838 | C2 | semidirect |
| 7. #19151808 | C2 | semidirect |
| 8. #19151752 | C2 | semidirect |
| 10. #103×D89 | C2 | semidirect |
| 11. C4×Q16×C89 | C2 | semidirect |
| 91. D356 | Q16 | semidirect |
| 123. C89 | #3299 | semidirect |
| 132. 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 |
| Q8×D356 | 2 |
| #19151949 | 2 |
| #19151935 | 2 |
| #19151893 | 2 |
| #19151838 | 2 |
| #19151808 | 2 |
| #19151752 | 2 |
| C8×D356 | 2 |
| #103×D89 | 2 |
| C4×Q16×C89 | 2 |
| #3299 | 89 |