Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668037 | C2 | semidirect |
| 2. C22×#13083559 | C2 | semidirect |
| 3. C2×#15668019 | C2 | semidirect |
| 4. #19151866 | C2 | direct (N × H) |
| 5. C2×#15667947 | C2 | semidirect |
| 6. C2×#15667929 | C2 | semidirect |
| 7. C2×#15667928 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C89 | C2 | semidirect |
| 11. #15668037 | C22 | semidirect |
| 17. C2×#13083559 | C22 | semidirect |
| 19. #15668019 | C22 | semidirect |
| 25. #15667947 | C22 | semidirect |
| 26. #15667929 | C22 | semidirect |
| 27. #15667928 | C22 | semidirect |
| 31. AGL(1,ℤ/8)×C89 | C22 | semidirect |
| 140. C2×C89 | #472 | semidirect |
| 144. C89 | C2×#472 | semidirect |
| 146. C2×AGL(1,ℤ/8) | D89 | semidirect |
| 159. AGL(1,ℤ/8) | C2×D89 | semidirect |
| 285. C2 | #19151866 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668037 | 2 |
| C22×#13083559 | 2 |
| C2×#15668019 | 2 |
| #19151866 | 2 |
| C2×#15667947 | 2 |
| C2×#15667929 | 2 |
| C2×#15667928 | 2 |
| C2×AGL(1,ℤ/8)×C89 | 2 |
| C2×#472 | 89 |