Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. Q8×Dic178 | C2 | semidirect |
| 3. #19151945 | C2 | semidirect |
| 4. #19151943 | C2 | semidirect |
| 5. #19151888 | C2 | semidirect |
| 6. #19151887 | C2 | semidirect |
| 7. #19151798 | C2 | semidirect |
| 8. #19151796 | C2 | semidirect |
| 9. C8×Dic178 | C2 | semidirect |
| 10. #19151683 | C2 | semidirect |
| 11. C4×SD16×C89 | C2 | semidirect |
| 77. Q8×C89 | #41 | semidirect |
| 99. Dic178 | SD16 | semidirect |
| 126. C89 | #3362 | semidirect |
| 137. C4×SD16 | D89 | semidirect |
| 206. Q8 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic178 | 2 |
| #19152269 | 2 |
| #19151945 | 2 |
| #19151943 | 2 |
| #19151888 | 2 |
| #19151887 | 2 |
| #19151798 | 2 |
| #19151796 | 2 |
| C8×Dic178 | 2 |
| #19151683 | 2 |
| C4×SD16×C89 | 2 |
| #3362 | 89 |