Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#64545 | C2 | semidirect |
| 2. C22×#64525 | C2 | semidirect |
| 3. C2×#10597384 | C2 | semidirect |
| 4. #11926688 | C2 | direct (N × H) |
| 5. C2×#10597292 | C2 | semidirect |
| 6. C2×#10597278 | C2 | semidirect |
| 7. C2×(C2×D19)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C19 | C2 | semidirect |
| 15. C2×#64545 | C22 | semidirect |
| 21. C2×SD16×C19 | C22 | semidirect |
| 25. #10597384 | C22 | semidirect |
| 27. C2×#64525 | C22 | semidirect |
| 30. #10597292 | C22 | semidirect |
| 31. #10597278 | C22 | semidirect |
| 32. (C2×D19)⋊C8 | C22 | semidirect |
| 38. C2×Q8×C19 | D4 | semidirect |
| 57. C2×D76 | D4 | semidirect |
| 89. Q8×C19 | C2×D4 | semidirect |
| 107. D76 | C2×D4 | semidirect |
| 138. C22×SD16 | D19 | semidirect |
| 146. C2×C19 | #449 | semidirect |
| 164. C2×SD16 | C2×D19 | semidirect |
| 176. C19 | C2×#449 | semidirect |
| 185. C2×Q8 | C22⋊D19 | semidirect |
| 233. Q8 | C2×C22⋊D19 | semidirect |
| 283. C2 | #11926688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#64545 | 2 |
| C22×#64525 | 2 |
| C2×#10597384 | 2 |
| #11926688 | 2 |
| C2×#10597292 | 2 |
| C2×#10597278 | 2 |
| C2×(C2×D19)⋊C8 | 2 |
| C22×SD16×C19 | 2 |
| C2×#449 | 19 |