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. #19151950 | C2 | semidirect |
| 4. #19151941 | C2 | semidirect |
| 5. #19151845 | C2 | semidirect |
| 6. #19151804 | C2 | semidirect |
| 7. #19151738 | C2 | semidirect |
| 8. C4×#13083561 | C2 | semidirect |
| 9. #19151675 | C2 | semidirect |
| 10. #19151605 | C2 | semidirect |
| 11. #477×C89 | C2 | semidirect |
| 127. C89 | #3329 | semidirect |
| 132. #477 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152314 | 2 |
| Q8×D356 | 2 |
| #19151950 | 2 |
| #19151941 | 2 |
| #19151845 | 2 |
| #19151804 | 2 |
| #19151738 | 2 |
| C4×#13083561 | 2 |
| #19151675 | 2 |
| #19151605 | 2 |
| #477×C89 | 2 |
| #3329 | 89 |