Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 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. #19152307 | C2 | semidirect |
| 2. #19152002 | C2 | semidirect |
| 3. #19152000 | C2 | semidirect |
| 4. #19151999 | C2 | semidirect |
| 5. #19151900 | C2 | semidirect |
| 6. #19151898 | C2 | semidirect |
| 7. #19151886 | C2 | semidirect |
| 8. C8×Dic178 | C2 | semidirect |
| 61. D8×C89 | Q8 | semidirect |
| 109. C89 | #3380 | semidirect |
| 154. D8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152307 | 2 |
| #19152002 | 2 |
| #19152000 | 2 |
| #19151999 | 2 |
| #19151900 | 2 |
| #19151898 | 2 |
| #19151886 | 2 |
| C8×Dic178 | 2 |
| D8×Dic89 | 2 |
| C4×D8×C89 | 2 |
| #3380 | 89 |