Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. C2×#15667999 | C2 | semidirect |
| 4. C2×#15667974 | C2 | semidirect |
| 5. #19151812 | C2 | direct (N × H) |
| 6. C2×#15667941 | C2 | semidirect |
| 7. C2×#15667935 | C2 | semidirect |
| 8. C2×#102×C89 | C2 | semidirect |
| 13. C2×#13083563 | C22 | semidirect |
| 18. #15667999 | C22 | semidirect |
| 20. #15667974 | C22 | semidirect |
| 25. #15667941 | C22 | semidirect |
| 26. #15667935 | C22 | semidirect |
| 30. #102×C89 | C22 | semidirect |
| 118. C2×C89 | #463 | semidirect |
| 124. C89 | C2×#463 | semidirect |
| 132. C2×#102 | D89 | semidirect |
| 154. #102 | C2×D89 | semidirect |
| 243. C2 | #19151812 | 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×#13083559 | 2 |
| C2×#15667999 | 2 |
| C2×#15667974 | 2 |
| #19151812 | 2 |
| C2×#15667941 | 2 |
| C2×#15667935 | 2 |
| C2×#102×C89 | 2 |
| C2×#463 | 89 |