Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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. #19152155 | C2 | semidirect |
| 3. #19151958 | C2 | semidirect |
| 4. #19151953 | C2 | semidirect |
| 5. #19151608 | C2 | semidirect |
| 7. C4×M16×C89 | C2 | semidirect |
| 10. #15668012 | C22 | semidirect |
| 11. #15668004 | C22 | semidirect |
| 19. #15667937 | C22 | semidirect |
| 23. #97×C89 | C22 | semidirect |
| 24. C4×C8×C89 | C22 | semidirect |
| 84. C89 | #3140 | semidirect |
| 91. C4×M16 | D89 | semidirect |
| 107. #97 | C2×D89 | semidirect |
| 108. C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152155 | 2 |
| C2×#15668000 | 2 |
| #19151958 | 2 |
| #19151953 | 2 |
| #19151608 | 2 |
| #19151604 | 2 |
| C4×M16×C89 | 2 |
| #3140 | 89 |