Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#15668034 | C2 | semidirect |
| 2. #19152028 | C2 | direct (N × H) |
| 3. C2×#15667958 | C2 | semidirect |
| 4. C2×#15667956 | C2 | semidirect |
| 5. C2×#15667955 | C2 | semidirect |
| 6. C2×#15667953 | C2 | semidirect |
| 7. C22×#13083549 | C2 | semidirect |
| 8. C2×#135×C89 | C2 | semidirect |
| 11. #15668034 | C22 | semidirect |
| 15. #15667958 | C22 | semidirect |
| 16. #15667956 | C22 | semidirect |
| 17. #15667955 | C22 | semidirect |
| 18. #15667953 | C22 | semidirect |
| 21. C2×#13083549 | C22 | semidirect |
| 24. #135×C89 | C22 | semidirect |
| 96. C2×C89 | #508 | semidirect |
| 100. C89 | C2×#508 | semidirect |
| 102. C2×#135 | D89 | semidirect |
| 114. #135 | C2×D89 | semidirect |
| 197. C2 | #19152028 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668034 | 2 |
| #19152028 | 2 |
| C2×#15667958 | 2 |
| C2×#15667956 | 2 |
| C2×#15667955 | 2 |
| C2×#15667953 | 2 |
| C22×#13083549 | 2 |
| C2×#135×C89 | 2 |
| C2×#508 | 89 |