Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D356 | C2 | semidirect |
| 2. C2×#15668040 | C2 | semidirect |
| 3. #19152109 | C2 | semidirect |
| 4. #19151751 | C2 | semidirect |
| 5. #19151734 | C2 | semidirect |
| 6. #19151604 | C2 | semidirect |
| 7. #407×C89 | C2 | semidirect |
| 9. C2×#13083574 | C22 | semidirect |
| 16. C2×#13083563 | C22 | semidirect |
| 17. C2×D712 | C22 | semidirect |
| 19. #15667991 | C22 | semidirect |
| 20. #15667986 | C22 | semidirect |
| 23. #15667971 | C22 | semidirect |
| 24. #15667934 | C22 | semidirect |
| 26. C2×M16×C89 | C22 | semidirect |
| 27. C22⋊C8×C89 | C22 | semidirect |
| 33. C2×Dic178 | C23 | semidirect |
| 40. C2×D356 | D4 | semidirect |
| 42. C2×D356 | C23 | semidirect |
| 48. C4⋊Dic89 | C23 | semidirect |
| 61. C2×C8×C89 | C23 | semidirect |
| 98. C22×C89 | AGL(1,ℤ/8) | semidirect |
| 118. C89 | #3003 | semidirect |
| 125. #407 | D89 | semidirect |
| 137. C2×M16 | C2×D89 | semidirect |
| 145. C22⋊C8 | C2×D89 | semidirect |
| 173. C2×C8 | C22×D89 | semidirect |
| 222. C22 | #15668040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D356 | 2 |
| C2×#15668040 | 2 |
| #19152109 | 2 |
| #19151751 | 2 |
| #19151734 | 2 |
| #19151604 | 2 |
| #407×C89 | 2 |
| #3003 | 89 |