Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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×D356 | C2 | semidirect |
| 3. #19151949 | C2 | semidirect |
| 4. #19151930 | C2 | semidirect |
| 5. #19151883 | C2 | semidirect |
| 6. #19151826 | C2 | semidirect |
| 7. #19151803 | C2 | semidirect |
| 8. #19151735 | C2 | semidirect |
| 9. C8×D356 | C2 | semidirect |
| 10. #103×D89 | C2 | semidirect |
| 11. C4×SD16×C89 | C2 | semidirect |
| 80. Q8×C89 | #41 | semidirect |
| 94. D356 | SD16 | semidirect |
| 129. C89 | #3298 | semidirect |
| 138. C4×SD16 | D89 | semidirect |
| 213. Q8 | #13083574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D356 | 2 |
| #19152253 | 2 |
| #19151949 | 2 |
| #19151930 | 2 |
| #19151883 | 2 |
| #19151826 | 2 |
| #19151803 | 2 |
| #19151735 | 2 |
| C8×D356 | 2 |
| #103×D89 | 2 |
| C4×SD16×C89 | 2 |
| #3298 | 89 |