Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15668045 | C2 | semidirect |
| 2. C2×#15668020 | C2 | semidirect |
| 4. #19152174 | C2 | semidirect |
| 5. #19151857 | C2 | semidirect |
| 6. #19151845 | C2 | semidirect |
| 7. #19151840 | C2 | semidirect |
| 8. #19151828 | C2 | semidirect |
| 9. #19151592 | C2 | semidirect |
| 10. C2×#15667935 | C2 | semidirect |
| 11. #428×C89 | C2 | semidirect |
| 77. M16×C89 | D4 | semidirect |
| 144. C89 | #3063 | semidirect |
| 153. #428 | D89 | semidirect |
| 210. M16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668045 | 2 |
| C2×#15668020 | 2 |
| #19152179 | 2 |
| #19152174 | 2 |
| #19151857 | 2 |
| #19151845 | 2 |
| #19151840 | 2 |
| #19151828 | 2 |
| #19151592 | 2 |
| C2×#15667935 | 2 |
| #428×C89 | 2 |
| #3063 | 89 |