Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×#64543 | C2 | semidirect |
| 2. C2×#10597358 | C2 | direct (N × H) |
| 3. C22×Dic76 | C2 | semidirect |
| 4. C22×#64526 | C2 | semidirect |
| 5. C22×C8×D19 | C2 | semidirect |
| 6. C22×D8×C19 | C2 | semidirect |
| 11. C2×#64543 | C22 | semidirect |
| 14. C2×D8×C19 | C22 | semidirect |
| 16. C2×#64526 | C22 | semidirect |
| 18. #10597358 | C22 | direct (N × H) |
| 19. C2×Dic76 | C22 | semidirect |
| 20. C2×C8×D19 | C22 | semidirect |
| 31. #64543 | C23 | semidirect |
| 36. D8×C19 | C23 | semidirect |
| 38. #64526 | C23 | semidirect |
| 40. Dic76 | C23 | semidirect |
| 41. C8×D19 | C23 | semidirect |
| 64. C22×C19 | #135 | semidirect |
| 76. C22×D8 | D19 | semidirect |
| 79. C2×C19 | C2×#135 | semidirect |
| 92. C2×D8 | C2×D19 | semidirect |
| 96. C19 | C22×#135 | semidirect |
| 114. D8 | C22×D19 | semidirect |
| 141. C22 | #10597358 | direct (N × H) |
| 149. C2 | C2×#10597358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64543 | 2 |
| C2×#10597358 | 2 |
| C22×Dic76 | 2 |
| C22×#64526 | 2 |
| C22×C8×D19 | 2 |
| C22×D8×C19 | 2 |
| C22×#135 | 19 |