Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #11926881 | C2 | direct (N × H) |
| 4. C2×#10597264 | C2 | semidirect |
| 5. C2×#10597273 | C2 | semidirect |
| 6. C2×#10597267 | C2 | semidirect |
| 8. C2×C19×#107 | C2 | semidirect |
| 24. C19×#107 | C22 | semidirect |
| 26. #10597273 | C22 | semidirect |
| 27. #10597267 | C22 | semidirect |
| 28. #10597264 | C22 | semidirect |
| 108. C2×#107 | D19 | semidirect |
| 112. C2×C19 | #484 | semidirect |
| 133. #107 | C2×D19 | semidirect |
| 137. C19 | C2×#484 | semidirect |
| 213. C2 | #11926881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597343 | 2 |
| C2×C4⋊C4×D19 | 2 |
| #11926881 | 2 |
| C2×#10597264 | 2 |
| C2×#10597273 | 2 |
| C2×#10597267 | 2 |
| C2×(C2×D19)⋊C8 | 2 |
| C2×C19×#107 | 2 |
| C2×#484 | 19 |