Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #19151949 | C2 | semidirect |
| 4. #19151934 | C2 | semidirect |
| 5. #19151894 | C2 | semidirect |
| 6. #19151839 | C2 | semidirect |
| 7. #19151809 | C2 | semidirect |
| 8. #19151756 | C2 | semidirect |
| 9. C4×Dic356 | C2 | semidirect |
| 10. C2×#15667937 | C2 | semidirect |
| 77. D4×C89 | Q16 | semidirect |
| 123. C89 | #3299 | semidirect |
| 208. D4 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152305 | 2 |
| D4×Dic178 | 2 |
| #19151949 | 2 |
| #19151934 | 2 |
| #19151894 | 2 |
| #19151839 | 2 |
| #19151809 | 2 |
| #19151756 | 2 |
| C4×Dic356 | 2 |
| C2×#15667937 | 2 |
| C8×D4×C89 | 2 |
| #3299 | 89 |