Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #19151616 | C2 | semidirect |
| 3. #19151614 | C2 | semidirect |
| 4. #19151603 | C2 | semidirect |
| 5. #19151580 | C2 | semidirect |
| 6. #19151571 | C2 | semidirect |
| 7. #418×C89 | C2 | semidirect |
| 15. C2×#13083573 | C4 | semidirect |
| 18. C2×D4×D89 | C4 | semidirect |
| 19. C2×#13083558 | C22 | semidirect |
| 20. #15667971 | C22 | semidirect |
| 28. C2×M16×C89 | C22 | semidirect |
| 29. #117×C89 | C22 | semidirect |
| 154. C89 | #1795 | semidirect |
| 159. #418 | D89 | semidirect |
| 175. C2×M16 | C2×D89 | semidirect |
| 177. #117 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668057 | 2 |
| #19151616 | 2 |
| #19151614 | 2 |
| #19151603 | 2 |
| #19151580 | 2 |
| #19151571 | 2 |
| #418×C89 | 2 |
| #1795 | 89 |