Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D8×D89 | C2 | semidirect |
| 2. #19152233 | C2 | semidirect |
| 3. #19151831 | C2 | semidirect |
| 4. #19151790 | C2 | semidirect |
| 5. #19151730 | C2 | semidirect |
| 6. C4×D712 | C2 | semidirect |
| 7. C8×D356 | C2 | semidirect |
| 8. #493×C89 | C2 | semidirect |
| 10. C2×D4×D89 | C22 | semidirect |
| 12. C2×#13083559 | C22 | semidirect |
| 14. C2×C8×D89 | C22 | semidirect |
| 16. #15667983 | C22 | semidirect |
| 19. C4×D356 | C22 | semidirect |
| 20. #15667946 | C22 | semidirect |
| 21. C4⋊#10623494 | C22 | semidirect |
| 22. #15667934 | C22 | semidirect |
| 23. #15667933 | C22 | semidirect |
| 24. #15667924 | C22 | semidirect |
| 25. C2×D8×C89 | C22 | semidirect |
| 26. C2×D8×C89 | C22 | semidirect |
| 27. #127×C89 | C22 | semidirect |
| 28. C4×C8×C89 | C22 | semidirect |
| 39. D712 | D4 | semidirect |
| 74. D356 | D8 | semidirect |
| 75. D356 | C2×D4 | semidirect |
| 80. C8×C89 | C2×D4 | semidirect |
| 92. C2×D89 | C2×D8 | semidirect |
| 94. C4×C89 | C2×D8 | semidirect |
| 106. C89 | D4×D8 | semidirect |
| 109. #493 | D89 | semidirect |
| 120. C2×D8 | C2×D89 | semidirect |
| 121. C2×D8 | C2×D89 | semidirect |
| 123. #127 | C2×D89 | semidirect |
| 134. C4×C8 | C2×D89 | semidirect |
| 187. C8 | D4×D89 | semidirect |
| 202. C4 | D8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D89 | 2 |
| #19152233 | 2 |
| #19151831 | 2 |
| #19151790 | 2 |
| #19151730 | 2 |
| C4×D712 | 2 |
| C8×D356 | 2 |
| #493×C89 | 2 |
| D4×D8 | 89 |