Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 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. C2×#10597353 | C2 | direct (N × H) |
| 3. C22×#64515 | C2 | semidirect |
| 4. C23×C19⋊C8 | C2 | semidirect |
| 5. C22×C8×D19 | C2 | semidirect |
| 6. C22×M16×C19 | C2 | semidirect |
| 14. C2×M16×C19 | C22 | semidirect |
| 18. C22×C19⋊C8 | C22 | semidirect |
| 19. #10597353 | C22 | direct (N × H) |
| 20. C2×#64515 | C22 | semidirect |
| 21. C2×C8×D19 | C22 | semidirect |
| 36. M16×C19 | C23 | semidirect |
| 40. C2×C19⋊C8 | C23 | semidirect |
| 41. #64515 | C23 | semidirect |
| 42. C8×D19 | C23 | semidirect |
| 64. C22×C19 | #131 | semidirect |
| 76. C22×M16 | D19 | semidirect |
| 80. C2×C19 | C2×#131 | semidirect |
| 92. C2×M16 | C2×D19 | semidirect |
| 98. C19 | C22×#131 | semidirect |
| 114. M16 | C22×D19 | semidirect |
| 142. C22 | #10597353 | direct (N × H) |
| 151. C2 | C2×#10597353 | 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 |
| C2×#10597353 | 2 |
| C22×#64515 | 2 |
| C23×C19⋊C8 | 2 |
| C22×C8×D19 | 2 |
| C22×M16×C19 | 2 |
| C22×#131 | 19 |