Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 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. C22×#13083563 | C2 | semidirect |
| 2. C22×#13083562 | C2 | semidirect |
| 4. C2×#15667977 | C2 | semidirect |
| 5. #19151797 | C2 | direct (N × H) |
| 6. C2×#15667941 | C2 | semidirect |
| 7. C2×#15667932 | C2 | semidirect |
| 8. C2×#102×C89 | C2 | semidirect |
| 14. C2×#13083563 | C22 | semidirect |
| 16. C2×#13083562 | C22 | semidirect |
| 21. #15667977 | C22 | semidirect |
| 25. #15667941 | C22 | semidirect |
| 26. #15667932 | C22 | semidirect |
| 30. #102×C89 | C22 | semidirect |
| 34. C2×Dic178 | D4 | semidirect |
| 89. C2×Dic89 | SD16 | semidirect |
| 97. Dic178 | C2×D4 | semidirect |
| 118. Dic89 | C2×SD16 | semidirect |
| 120. C2×C89 | #460 | semidirect |
| 126. C89 | C2×#460 | semidirect |
| 134. C2×#102 | D89 | semidirect |
| 156. #102 | C2×D89 | semidirect |
| 247. C2 | #19151797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083563 | 2 |
| C22×#13083562 | 2 |
| C2×#15668008 | 2 |
| C2×#15667977 | 2 |
| #19151797 | 2 |
| C2×#15667941 | 2 |
| C2×#15667932 | 2 |
| C2×#102×C89 | 2 |
| C2×#460 | 89 |