Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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. Q8×D356 | C2 | semidirect |
| 3. #19151958 | C2 | semidirect |
| 4. #19151945 | C2 | semidirect |
| 5. #19151889 | C2 | semidirect |
| 6. #19151884 | C2 | semidirect |
| 7. #19151814 | C2 | semidirect |
| 9. #19151711 | C2 | semidirect |
| 10. C4×#13083563 | C2 | semidirect |
| 11. #446×C89 | C2 | semidirect |
| 125. C89 | #3373 | semidirect |
| 134. #446 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152333 | 2 |
| Q8×D356 | 2 |
| #19151958 | 2 |
| #19151945 | 2 |
| #19151889 | 2 |
| #19151884 | 2 |
| #19151814 | 2 |
| #19151794 | 2 |
| #19151711 | 2 |
| C4×#13083563 | 2 |
| #446×C89 | 2 |
| #3373 | 89 |