Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #19152333 | C2 | semidirect |
| 2. #19151980 | C2 | semidirect |
| 3. #19151972 | C2 | semidirect |
| 4. #19151820 | C2 | semidirect |
| 5. #19151810 | C2 | semidirect |
| 6. #19151805 | C2 | semidirect |
| 8. Q8×#10623494 | C2 | semidirect |
| 9. C4×#13083561 | C2 | semidirect |
| 10. C4×#13083562 | C2 | semidirect |
| 11. #556×C89 | C2 | semidirect |
| 126. C89 | #3394 | semidirect |
| 128. #556 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152333 | 2 |
| #19151980 | 2 |
| #19151972 | 2 |
| #19151820 | 2 |
| #19151810 | 2 |
| #19151805 | 2 |
| #19151793 | 2 |
| Q8×#10623494 | 2 |
| C4×#13083561 | 2 |
| C4×#13083562 | 2 |
| #556×C89 | 2 |
| #3394 | 89 |