Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 526 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. C2×#15668035 | C2 | semidirect |
| 2. C22×D712 | C2 | semidirect |
| 3. #19152239 | C2 | semidirect |
| 4. #19151983 | C2 | semidirect |
| 5. #19151835 | C2 | semidirect |
| 6. #19151816 | C2 | semidirect |
| 7. #19151748 | C2 | semidirect |
| 8. #19151746 | C2 | semidirect |
| 9. #19151680 | C2 | semidirect |
| 10. C8×C22⋊D89 | C2 | semidirect |
| 11. #467×C89 | C2 | semidirect |
| 12. C2×#13083575 | C22 | semidirect |
| 15. C2×#13083561 | C22 | semidirect |
| 16. C2×#13083561 | C22 | semidirect |
| 21. C2×C8×D89 | C22 | semidirect |
| 22. #15668001 | C22 | semidirect |
| 25. #15667987 | C22 | semidirect |
| 27. #15667974 | C22 | semidirect |
| 30. #15667941 | C22 | semidirect |
| 31. #15667932 | C22 | semidirect |
| 32. #15667932 | C22 | semidirect |
| 34. #15667924 | C22 | semidirect |
| 35. C8×Dic89 | C22 | semidirect |
| 36. C2×Q16×C89 | C22 | semidirect |
| 39. #107×C89 | C22 | semidirect |
| 40. #103×C89 | C22 | semidirect |
| 59. D712 | D4 | semidirect |
| 116. C22×C89 | #135 | semidirect |
| 144. C89 | #3280 | semidirect |
| 149. #467 | D89 | semidirect |
| 159. C2×Q16 | C2×D89 | semidirect |
| 177. #107 | C2×D89 | semidirect |
| 179. #103 | C2×D89 | semidirect |
| 270. C22 | #15668035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668035 | 2 |
| C22×D712 | 2 |
| #19152239 | 2 |
| #19151983 | 2 |
| #19151835 | 2 |
| #19151816 | 2 |
| #19151748 | 2 |
| #19151746 | 2 |
| #19151680 | 2 |
| C8×C22⋊D89 | 2 |
| #467×C89 | 2 |
| #3280 | 89 |