Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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. C22×#13083574 | C2 | semidirect |
| 2. C2×#15668038 | C2 | direct (N × H) |
| 3. C22×#13083562 | C2 | semidirect |
| 4. C22×#13083559 | C2 | semidirect |
| 5. C22×#13083558 | C2 | semidirect |
| 6. C23×D4×C89 | C2 | semidirect |
| 8. C2×#13083574 | C22 | semidirect |
| 9. C22×Dic178 | C22 | semidirect |
| 10. C22×D356 | C22 | semidirect |
| 13. #15668038 | C22 | direct (N × H) |
| 14. C2×#13083562 | C22 | semidirect |
| 15. C2×#13083559 | C22 | semidirect |
| 16. C2×#13083558 | C22 | semidirect |
| 17. C22×#10623494 | C22 | semidirect |
| 22. C22×D4×C89 | C22 | semidirect |
| 26. #13083574 | C23 | semidirect |
| 28. C2×Dic178 | C23 | semidirect |
| 30. C2×D356 | C23 | semidirect |
| 34. #13083562 | C23 | semidirect |
| 35. #13083559 | C23 | semidirect |
| 36. #13083558 | C23 | semidirect |
| 37. C2×#10623494 | C23 | semidirect |
| 46. C2×D4×C89 | C23 | semidirect |
| 71. D356 | C24 | semidirect |
| 74. Dic178 | C24 | semidirect |
| 75. #10623494 | C24 | semidirect |
| 80. C22×C89 | AGL(1,ℤ/8) | semidirect |
| 91. C2×C89 | C2×AGL(1,ℤ/8) | semidirect |
| 95. C89 | C22×AGL(1,ℤ/8) | semidirect |
| 97. C23×D4 | D89 | semidirect |
| 111. C22×D4 | C2×D89 | semidirect |
| 135. C2×D4 | C22×D89 | semidirect |
| 177. C22 | #15668038 | direct (N × H) |
| 187. C2 | C2×#15668038 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C2×#15668038 | 2 |
| C22×#13083562 | 2 |
| C22×#13083559 | 2 |
| C22×#13083558 | 2 |
| C23×D4×C89 | 2 |
| C22×AGL(1,ℤ/8) | 89 |