Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 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×#10597365 | C2 | semidirect |
| 2. C2×#10597358 | C2 | semidirect |
| 3. #11926975 | C2 | direct (N × H) |
| 4. C2×#10597286 | C2 | semidirect |
| 5. C2×#10597257 | C2 | semidirect |
| 6. C2×#10597283 | C2 | semidirect |
| 7. C2×C16×D19 | C2 | semidirect |
| 8. C2×C19×SD32 | C2 | semidirect |
| 16. #10597365 | C22 | semidirect |
| 18. #10597358 | C22 | semidirect |
| 22. C19×SD32 | C22 | semidirect |
| 24. #10597286 | C22 | semidirect |
| 25. #10597283 | C22 | semidirect |
| 27. #10597257 | C22 | semidirect |
| 28. C16×D19 | C22 | semidirect |
| 100. C2×SD32 | D19 | semidirect |
| 104. C2×C19 | #508 | semidirect |
| 123. SD32 | C2×D19 | semidirect |
| 128. C19 | C2×#508 | semidirect |
| 197. C2 | #11926975 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597365 | 2 |
| C2×#10597358 | 2 |
| #11926975 | 2 |
| C2×#10597286 | 2 |
| C2×#10597257 | 2 |
| C2×#10597283 | 2 |
| C2×C16×D19 | 2 |
| C2×C19×SD32 | 2 |
| C2×#508 | 19 |