Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#15668032 | C2 | semidirect |
| 2. #19152269 | C2 | semidirect |
| 3. #19151974 | C2 | semidirect |
| 4. #19151832 | C2 | semidirect |
| 5. #19151798 | C2 | semidirect |
| 6. #19151795 | C2 | semidirect |
| 7. #19151743 | C2 | semidirect |
| 8. #19151741 | C2 | semidirect |
| 9. C4×#13083564 | C2 | semidirect |
| 10. D4×#10623494 | C2 | semidirect |
| 11. #550×C89 | C2 | semidirect |
| 51. #13083564 | D4 | semidirect |
| 131. C4×C89 | #135 | semidirect |
| 143. C89 | #3287 | semidirect |
| 146. #550 | D89 | semidirect |
| 276. C4 | #15668032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668032 | 2 |
| #19152269 | 2 |
| #19151974 | 2 |
| #19151832 | 2 |
| #19151798 | 2 |
| #19151795 | 2 |
| #19151743 | 2 |
| #19151741 | 2 |
| C4×#13083564 | 2 |
| D4×#10623494 | 2 |
| #550×C89 | 2 |
| #3287 | 89 |