Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4⋊Q8×D89 | C2 | semidirect |
| 3. #19151960 | C2 | semidirect |
| 4. #19151959 | C2 | semidirect |
| 5. #19151958 | C2 | semidirect |
| 6. #19151957 | C2 | semidirect |
| 7. #19151956 | C2 | semidirect |
| 8. #103×D89 | C2 | semidirect |
| 10. #97×D89 | C2 | semidirect |
| 11. #489×C89 | C2 | semidirect |
| 16. #15668012 | C22 | semidirect |
| 18. #15668011 | C22 | semidirect |
| 30. #15667937 | C22 | semidirect |
| 31. #15667936 | C22 | semidirect |
| 32. #15667935 | C22 | semidirect |
| 36. #15667923 | C22 | semidirect |
| 37. #15667922 | C22 | semidirect |
| 38. C4⋊Q8×C89 | C22 | semidirect |
| 40. #103×C89 | C22 | semidirect |
| 42. #97×C89 | C22 | semidirect |
| 140. D89 | #489 | direct (N × H) |
| 142. C89 | C2×#489 | semidirect |
| 150. #489 | D89 | direct (N × H) |
| 162. C4⋊Q8 | C2×D89 | semidirect |
| 177. #103 | C2×D89 | semidirect |
| 184. #97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D89 | 2 |
| #124×D89 | 2 |
| #19151960 | 2 |
| #19151959 | 2 |
| #19151958 | 2 |
| #19151957 | 2 |
| #19151956 | 2 |
| #103×D89 | 2 |
| #102×D89 | 2 |
| #97×D89 | 2 |
| #489×C89 | 2 |
| C2×#489 | 89 |