Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15668040 | C2 | semidirect |
| 2. C2×#15668038 | C2 | semidirect |
| 3. C2×#15668008 | C2 | semidirect |
| 4. #19152066 | C2 | semidirect |
| 5. #19151797 | C2 | semidirect |
| 6. #19151792 | C2 | semidirect |
| 7. #19151621 | C2 | semidirect |
| 8. #19151602 | C2 | semidirect |
| 9. #418×C89 | C2 | semidirect |
| 15. C2×#13083563 | C22 | semidirect |
| 16. C2×#13083562 | C22 | semidirect |
| 17. C2×D712 | C22 | semidirect |
| 18. C2×#13083559 | C22 | semidirect |
| 23. #15667977 | C22 | semidirect |
| 24. #15667974 | C22 | semidirect |
| 29. #15667941 | C22 | semidirect |
| 30. #15667932 | C22 | semidirect |
| 34. #102×C89 | C22 | semidirect |
| 37. #13083574 | D4 | semidirect |
| 101. D356 | C2×D4 | semidirect |
| 105. Dic178 | C2×D4 | semidirect |
| 125. Dic89 | AGL(1,ℤ/8) | semidirect |
| 133. C89 | #3038 | semidirect |
| 142. #418 | D89 | semidirect |
| 167. #102 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668040 | 2 |
| C2×#15668038 | 2 |
| C2×#15668008 | 2 |
| #19152066 | 2 |
| #19151797 | 2 |
| #19151792 | 2 |
| #19151621 | 2 |
| #19151602 | 2 |
| #418×C89 | 2 |
| #3038 | 89 |