Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #19152039 | C2 | semidirect |
| 3. C2×#15667955 | C2 | semidirect |
| 4. #19151410 | C2 | semidirect |
| 5. #19151404 | C2 | semidirect |
| 6. #19151382 | C2 | semidirect |
| 7. #473×C89 | C2 | semidirect |
| 18. #15667952 | C22 | semidirect |
| 19. C2×#13083549 | C22 | semidirect |
| 21. C2×Q16×C89 | C22 | semidirect |
| 23. #108×C89 | C22 | semidirect |
| 92. C89 | #2194 | semidirect |
| 96. #473 | D89 | semidirect |
| 106. C2×Q16 | C2×D89 | semidirect |
| 115. #108 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152403 | 2 |
| #19152039 | 2 |
| C2×#15667955 | 2 |
| #19151410 | 2 |
| #19151404 | 2 |
| #19151382 | 2 |
| #473×C89 | 2 |
| #2194 | 89 |