Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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×C4×Dic38 | C2 | semidirect |
| 4. C4×#64516 | C2 | direct (N × H) |
| 5. C2×#10597274 | C2 | semidirect |
| 6. C2×#10597273 | C2 | semidirect |
| 8. C2×C4×C8×C19 | C2 | semidirect |
| 20. C2×#64516 | C4 | direct (N × H) |
| 25. C4×Dic38 | C22 | semidirect |
| 26. C4×C8×C19 | C22 | semidirect |
| 28. #10597274 | C22 | semidirect |
| 29. #10597273 | C22 | semidirect |
| 45. C2×Dic38 | C2×C4 | semidirect |
| 48. C2×C8×C19 | C2×C4 | semidirect |
| 60. #64516 | C2×C4 | direct (N × H) |
| 67. C2×C4×C19 | SD16 | semidirect |
| 86. Dic38 | C22×C4 | semidirect |
| 88. C8×C19 | C22×C4 | semidirect |
| 100. C4×C19 | C2×SD16 | semidirect |
| 113. C2×C4×C8 | D19 | semidirect |
| 114. C2×C19 | C4×SD16 | semidirect |
| 139. C4×C8 | C2×D19 | semidirect |
| 140. C19 | C2×C4×SD16 | semidirect |
| 160. C2×C8 | C4×D19 | semidirect |
| 191. C2×C4 | #64516 | direct (N × H) |
| 199. C8 | C2×C4×D19 | semidirect |
| 213. C4 | C2×#64516 | direct (N × H) |
| 217. C2 | C4×#64516 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64516 | 2 |
| C2×C4×Dic38 | 2 |
| C2×C4×D76 | 2 |
| C4×#64516 | 2 |
| C2×#10597274 | 2 |
| C2×#10597273 | 2 |
| C2×#10597278 | 2 |
| C2×C4×C8×C19 | 2 |
| C2×C4×SD16 | 19 |