Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D89 | C2 | semidirect |
| 3. C2×#15667940 | C2 | semidirect |
| 4. C2×#15667938 | C2 | semidirect |
| 5. C4×#13083551 | C2 | semidirect |
| 6. #19151357 | C2 | semidirect |
| 7. #339×C89 | C2 | semidirect |
| 16. #15667992 | C4 | semidirect |
| 17. #15667992 | C4 | semidirect |
| 18. #15667987 | C4 | semidirect |
| 19. #15667987 | C4 | semidirect |
| 53. #13083558 | D4 | semidirect |
| 69. M16×C89 | D4 | semidirect |
| 139. C2×D89 | #104 | semidirect |
| 160. C89 | #1871 | semidirect |
| 167. #339 | D89 | semidirect |
| 218. M16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D89 | 2 |
| #19152110 | 2 |
| C2×#15667940 | 2 |
| C2×#15667938 | 2 |
| C4×#13083551 | 2 |
| #19151357 | 2 |
| #339×C89 | 2 |
| #1871 | 89 |