Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 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. Q8×Dic178 | C2 | semidirect |
| 3. #19152007 | C2 | semidirect |
| 4. #19152003 | C2 | semidirect |
| 5. #19151906 | C2 | semidirect |
| 6. #19151894 | C2 | semidirect |
| 11. #446×C89 | C2 | semidirect |
| 48. #13083563 | Q8 | semidirect |
| 116. C89 | #3385 | semidirect |
| 125. #446 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic178 | 2 |
| #19152308 | 2 |
| #19152007 | 2 |
| #19152003 | 2 |
| #19151906 | 2 |
| #19151894 | 2 |
| #19151889 | 2 |
| #19151879 | 2 |
| #19151700 | 2 |
| C4×#13083563 | 2 |
| #446×C89 | 2 |
| #3385 | 89 |