Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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. #19152148 | C2 | semidirect |
| 2. C2×#15668009 | C2 | semidirect |
| 3. #19151975 | C2 | semidirect |
| 4. #19151945 | C2 | semidirect |
| 5. #19151794 | C2 | semidirect |
| 6. #19151734 | C2 | semidirect |
| 7. #431×C89 | C2 | semidirect |
| 12. C2×D712 | C22 | semidirect |
| 13. #15668012 | C22 | semidirect |
| 18. #15668009 | C22 | semidirect |
| 23. C4×D356 | C22 | semidirect |
| 24. #15667934 | C22 | semidirect |
| 26. C4⋊C8×C89 | C22 | semidirect |
| 28. C4×C8×C89 | C22 | semidirect |
| 67. C2×C4×C89 | D8 | semidirect |
| 113. C89 | #3205 | semidirect |
| 120. #431 | D89 | semidirect |
| 138. C4⋊C8 | C2×D89 | semidirect |
| 141. C4×C8 | C2×D89 | semidirect |
| 193. C2×C4 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152148 | 2 |
| C2×#15668009 | 2 |
| #19151975 | 2 |
| #19151945 | 2 |
| #19151794 | 2 |
| #19151734 | 2 |
| #431×C89 | 2 |
| #3205 | 89 |