Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Q16×D89 | C2 | semidirect |
| 3. #19152040 | C2 | direct (N × H) |
| 4. C2×#15667958 | C2 | semidirect |
| 5. C2×#15667957 | C2 | semidirect |
| 6. C2×#15667955 | C2 | semidirect |
| 7. C2×#15667951 | C2 | semidirect |
| 8. C2×Q32×C89 | C2 | semidirect |
| 16. Q16×D89 | C22 | semidirect |
| 20. #15667958 | C22 | semidirect |
| 21. #15667957 | C22 | semidirect |
| 22. #15667955 | C22 | semidirect |
| 23. #15667951 | C22 | semidirect |
| 27. Q32×C89 | C22 | semidirect |
| 93. C2×C89 | #510 | semidirect |
| 98. C89 | C2×#510 | semidirect |
| 103. C2×Q32 | D89 | semidirect |
| 121. Q32 | C2×D89 | semidirect |
| 193. C2 | #19152040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668035 | 2 |
| C2×Q16×D89 | 2 |
| #19152040 | 2 |
| C2×#15667958 | 2 |
| C2×#15667957 | 2 |
| C2×#15667955 | 2 |
| C2×#15667951 | 2 |
| C2×Q32×C89 | 2 |
| C2×#510 | 89 |