Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13083574 | C2 | semidirect |
| 2. C2×#15668040 | C2 | semidirect |
| 3. C2×#15667986 | C2 | semidirect |
| 4. #19151745 | C2 | semidirect |
| 5. #19151739 | C2 | semidirect |
| 6. #19151734 | C2 | semidirect |
| 7. #19151600 | C2 | semidirect |
| 8. #407×C89 | C2 | semidirect |
| 13. C2×#13083574 | C22 | semidirect |
| 14. C22×Dic178 | C22 | semidirect |
| 15. C22×D356 | C22 | semidirect |
| 16. C22×D356 | C22 | semidirect |
| 21. C2×#13083563 | C22 | semidirect |
| 22. C2×D712 | C22 | semidirect |
| 26. #15667986 | C22 | semidirect |
| 27. C2×C4⋊Dic89 | C22 | semidirect |
| 29. #15667937 | C22 | semidirect |
| 30. #15667934 | C22 | semidirect |
| 32. C2×M16×C89 | C22 | semidirect |
| 33. C22⋊C8×C89 | C22 | semidirect |
| 34. C22⋊C8×C89 | C22 | semidirect |
| 42. #13083574 | D4 | semidirect |
| 115. D356 | C2×D4 | semidirect |
| 120. Dic178 | C2×D4 | semidirect |
| 131. C22×C89 | AGL(1,ℤ/8) | semidirect |
| 156. C89 | #3006 | semidirect |
| 164. #407 | D89 | semidirect |
| 180. C2×M16 | C2×D89 | semidirect |
| 189. C22⋊C8 | C2×D89 | semidirect |
| 190. C22⋊C8 | C2×D89 | semidirect |
| 295. C22 | #15668040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C2×#15668040 | 2 |
| C2×#15667986 | 2 |
| #19151745 | 2 |
| #19151739 | 2 |
| #19151734 | 2 |
| #19151600 | 2 |
| #407×C89 | 2 |
| #3006 | 89 |