Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#15668035 | C2 | semidirect |
| 2. #19152149 | C2 | semidirect |
| 3. C4×#13083575 | C2 | semidirect |
| 4. #19151822 | C2 | semidirect |
| 5. #19151816 | C2 | semidirect |
| 6. #19151800 | C2 | semidirect |
| 7. #19151798 | C2 | semidirect |
| 8. #19151794 | C2 | semidirect |
| 9. C4⋊C8×D89 | C2 | semidirect |
| 10. #19151593 | C2 | semidirect |
| 11. #462×C89 | C2 | semidirect |
| 47. #13083575 | D4 | semidirect |
| 137. C4×C89 | #135 | semidirect |
| 151. C89 | #3035 | semidirect |
| 157. #462 | D89 | semidirect |
| 292. C4 | #15668035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668035 | 2 |
| #19152149 | 2 |
| C4×#13083575 | 2 |
| #19151822 | 2 |
| #19151816 | 2 |
| #19151800 | 2 |
| #19151798 | 2 |
| #19151794 | 2 |
| C4⋊C8×D89 | 2 |
| #19151593 | 2 |
| #462×C89 | 2 |
| #3035 | 89 |