Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13083575 | C2 | semidirect |
| 2. C2×#15668035 | C2 | semidirect |
| 3. #19152111 | C2 | semidirect |
| 4. #19151759 | C2 | semidirect |
| 5. #19151748 | C2 | semidirect |
| 6. #19151746 | C2 | semidirect |
| 7. #19151737 | C2 | semidirect |
| 8. #19151734 | C2 | semidirect |
| 9. #19151593 | C2 | semidirect |
| 10. C22⋊C8×D89 | C2 | semidirect |
| 11. #451×C89 | C2 | semidirect |
| 17. C2×#13083575 | C22 | semidirect |
| 23. C2×#13083561 | C22 | semidirect |
| 24. C2×#13083561 | C22 | semidirect |
| 25. C2×D712 | C22 | semidirect |
| 26. C2×C8×D89 | C22 | semidirect |
| 28. #15667988 | C22 | semidirect |
| 29. #15667987 | C22 | semidirect |
| 34. #15667970 | C22 | semidirect |
| 35. #15667936 | C22 | semidirect |
| 36. #15667934 | C22 | semidirect |
| 37. #15667932 | C22 | semidirect |
| 39. #15667924 | C22 | semidirect |
| 41. C2×Q16×C89 | C22 | semidirect |
| 43. #103×C89 | C22 | semidirect |
| 53. #13083575 | D4 | semidirect |
| 143. C22×C89 | #135 | semidirect |
| 176. C89 | #3002 | semidirect |
| 181. #451 | D89 | semidirect |
| 200. C2×Q16 | C2×D89 | semidirect |
| 215. #103 | C2×D89 | semidirect |
| 333. C22 | #15668035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083575 | 2 |
| C2×#15668035 | 2 |
| #19152111 | 2 |
| #19151759 | 2 |
| #19151748 | 2 |
| #19151746 | 2 |
| #19151737 | 2 |
| #19151734 | 2 |
| #19151593 | 2 |
| C22⋊C8×D89 | 2 |
| #451×C89 | 2 |
| #3002 | 89 |