Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#10597358 | C2 | semidirect |
| 2. C2×D8×D19 | C2 | semidirect |
| 3. #11926978 | C2 | direct (N × H) |
| 4. C2×#10597257 | C2 | semidirect |
| 5. C2×#10597284 | C2 | semidirect |
| 6. C2×#10597283 | C2 | semidirect |
| 7. C2×#10597255 | C2 | semidirect |
| 8. C2×C19×D16 | C2 | semidirect |
| 12. C2×D8×C19 | C22 | semidirect |
| 16. #10597358 | C22 | semidirect |
| 18. D8×D19 | C22 | semidirect |
| 19. C2×Dic76 | C22 | semidirect |
| 22. C19×D16 | C22 | semidirect |
| 23. C2×C16×C19 | C22 | semidirect |
| 24. #10597284 | C22 | semidirect |
| 25. #10597283 | C22 | semidirect |
| 26. C2×C19⋊C16 | C22 | semidirect |
| 27. #10597257 | C22 | semidirect |
| 28. #10597255 | C22 | semidirect |
| 45. D8×C19 | C23 | semidirect |
| 51. Dic76 | C23 | semidirect |
| 56. C16×C19 | C23 | semidirect |
| 57. C19⋊C16 | C23 | semidirect |
| 104. C2×D16 | D19 | semidirect |
| 108. C2×C19 | #509 | semidirect |
| 123. C2×D8 | C2×D19 | semidirect |
| 128. D16 | C2×D19 | semidirect |
| 131. C2×C16 | C2×D19 | semidirect |
| 132. C19 | C2×#509 | semidirect |
| 155. D8 | C22×D19 | semidirect |
| 161. C16 | C22×D19 | semidirect |
| 205. C2 | #11926978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597358 | 2 |
| C2×D8×D19 | 2 |
| #11926978 | 2 |
| C2×#10597257 | 2 |
| C2×#10597284 | 2 |
| C2×#10597283 | 2 |
| C2×#10597255 | 2 |
| C2×C19×D16 | 2 |
| C2×#509 | 19 |