Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. Q8×D356 | C2 | semidirect |
| 3. #19151949 | C2 | semidirect |
| 4. #19151942 | C2 | semidirect |
| 5. #19151893 | C2 | semidirect |
| 6. #19151843 | C2 | semidirect |
| 7. #19151803 | C2 | semidirect |
| 8. #19151735 | C2 | semidirect |
| 9. #19151677 | C2 | semidirect |
| 10. #19151605 | C2 | semidirect |
| 11. C4×SD16×C89 | C2 | semidirect |
| 127. C89 | #3329 | semidirect |
| 136. C4×SD16 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152313 | 2 |
| Q8×D356 | 2 |
| #19151949 | 2 |
| #19151942 | 2 |
| #19151893 | 2 |
| #19151843 | 2 |
| #19151803 | 2 |
| #19151735 | 2 |
| #19151677 | 2 |
| #19151605 | 2 |
| C4×SD16×C89 | 2 |
| #3329 | 89 |