Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 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×#15668044 | C2 | semidirect |
| 2. C2×#15668039 | C2 | semidirect |
| 3. #19152149 | C2 | semidirect |
| 4. #124×D89 | C2 | semidirect |
| 5. #19151990 | C2 | semidirect |
| 6. #19151988 | C2 | semidirect |
| 7. #19151987 | C2 | semidirect |
| 8. #19151983 | C2 | semidirect |
| 9. #19151979 | C2 | semidirect |
| 10. #19151550 | C2 | semidirect |
| 11. #497×C89 | C2 | semidirect |
| 17. C2×#13083564 | C22 | semidirect |
| 18. C2×#13083563 | C22 | semidirect |
| 20. C2×#13083561 | C22 | semidirect |
| 24. #15668009 | C22 | semidirect |
| 26. #15668001 | C22 | semidirect |
| 34. #15667923 | C22 | semidirect |
| 35. C8×Dic89 | C22 | semidirect |
| 36. C2×Q16×C89 | C22 | semidirect |
| 38. C4⋊Q8×C89 | C22 | semidirect |
| 40. #97×C89 | C22 | semidirect |
| 63. #13083557 | D4 | semidirect |
| 135. C89 | #3153 | semidirect |
| 141. #497 | D89 | semidirect |
| 153. C2×Q16 | C2×D89 | semidirect |
| 161. C4⋊Q8 | C2×D89 | semidirect |
| 174. #97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668044 | 2 |
| C2×#15668039 | 2 |
| #19152149 | 2 |
| #124×D89 | 2 |
| #19151990 | 2 |
| #19151988 | 2 |
| #19151987 | 2 |
| #19151983 | 2 |
| #19151979 | 2 |
| #19151550 | 2 |
| #497×C89 | 2 |
| #3153 | 89 |