Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 2. C23×Dic178 | C2 | semidirect |
| 3. C2×#15668045 | C2 | direct (N × H) |
| 4. C22×Dic356 | C2 | semidirect |
| 5. C22×#13083563 | C2 | semidirect |
| 6. C22×M16×C89 | C2 | semidirect |
| 13. C22×Dic178 | C22 | semidirect |
| 18. #15668045 | C22 | direct (N × H) |
| 19. C2×Dic356 | C22 | semidirect |
| 20. C2×#13083563 | C22 | semidirect |
| 22. C2×M16×C89 | C22 | semidirect |
| 33. C2×Dic178 | C23 | semidirect |
| 41. Dic356 | C23 | semidirect |
| 42. #13083563 | C23 | semidirect |
| 48. M16×C89 | C23 | semidirect |
| 74. C22×C89 | #137 | semidirect |
| 85. C2×C89 | C2×#137 | semidirect |
| 89. C89 | C22×#137 | semidirect |
| 95. C22×M16 | D89 | semidirect |
| 111. C2×M16 | C2×D89 | semidirect |
| 137. M16 | C22×D89 | semidirect |
| 165. C22 | #15668045 | direct (N × H) |
| 175. C2 | C2×#15668045 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13083574 | 2 |
| C23×Dic178 | 2 |
| C2×#15668045 | 2 |
| C22×Dic356 | 2 |
| C22×#13083563 | 2 |
| C22×M16×C89 | 2 |
| C22×#137 | 89 |