Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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. C8×D628 | C2 | semidirect |
| 3. #23757026 | C2 | semidirect |
| 4. #23757002 | C2 | semidirect |
| 5. C82×C157 | C2 | semidirect |
| 18. D1256 | C8 | direct (N × H) |
| 31. D628 | C2×C8 | semidirect |
| 42. C8×C157 | C2×C8 | semidirect |
| 43. C8×C157 | D8 | semidirect |
| 58. C157 | C8×D8 | semidirect |
| 64. C82 | D157 | semidirect |
| 101. C8 | C8×D157 | semidirect |
| 102. C8 | D1256 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1256 | 2 |
| C8×D628 | 2 |
| #23757026 | 2 |
| #23757002 | 2 |
| C82×C157 | 2 |
| C8×D8 | 157 |