Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 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. #19152348 | C2 | direct (N × H) |
| 2. C2×#15668010 | C2 | semidirect |
| 3. C2×#15668005 | C2 | semidirect |
| 4. C2×#15668004 | C2 | semidirect |
| 6. C2×#15667989 | C2 | semidirect |
| 10. #15668010 | C22 | semidirect |
| 11. #15668005 | C22 | semidirect |
| 12. #15668004 | C22 | semidirect |
| 14. #15667989 | C22 | semidirect |
| 82. C2×C89 | #563 | semidirect |
| 86. C89 | C2×#563 | semidirect |
| 168. C2 | #19152348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152348 | 2 |
| C2×#15668010 | 2 |
| C2×#15668005 | 2 |
| C2×#15668004 | 2 |
| C2×#15667993 | 2 |
| C2×#15667989 | 2 |
| C2×#124×C89 | 2 |
| C2×#563 | 89 |