Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
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×Dic38 | C2 | semidirect |
| 3. C2×#10597355 | C2 | direct (N × H) |
| 4. C22×Dic76 | C2 | semidirect |
| 5. C22×#64516 | C2 | semidirect |
| 6. C22×M16×C19 | C2 | semidirect |
| 18. C22×Dic38 | C22 | semidirect |
| 19. C2×M16×C19 | C22 | semidirect |
| 21. #10597355 | C22 | direct (N × H) |
| 22. C2×Dic76 | C22 | semidirect |
| 23. C2×#64516 | C22 | semidirect |
| 45. C2×Dic38 | C23 | semidirect |
| 46. M16×C19 | C23 | semidirect |
| 48. Dic76 | C23 | semidirect |
| 49. #64516 | C23 | semidirect |
| 75. C22×C19 | #137 | semidirect |
| 90. C22×M16 | D19 | semidirect |
| 92. C2×C19 | C2×#137 | semidirect |
| 110. C2×M16 | C2×D19 | semidirect |
| 112. C19 | C22×#137 | semidirect |
| 137. M16 | C22×D19 | semidirect |
| 165. C22 | #10597355 | direct (N × H) |
| 175. C2 | C2×#10597355 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64541 | 2 |
| C23×Dic38 | 2 |
| C2×#10597355 | 2 |
| C22×Dic76 | 2 |
| C22×#64516 | 2 |
| C22×M16×C19 | 2 |
| C22×#137 | 19 |