Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D317 | C2 | semidirect |
| 2. C2×#19099563 | C2 | semidirect |
| 3. C2×#19099561 | C2 | semidirect |
| 5. #23778703 | C2 | semidirect |
| 6. #23778692 | C2 | semidirect |
| 7. #103×C317 | C2 | semidirect |
| 27. Dic634 | D4 | semidirect |
| 38. Q8×C317 | D4 | semidirect |
| 49. C2×D317 | SD16 | semidirect |
| 61. C317 | #448 | semidirect |
| 68. #103 | D317 | semidirect |
| 91. Q8 | D1268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D317 | 2 |
| C2×#19099563 | 2 |
| C2×#19099561 | 2 |
| #23778755 | 2 |
| #23778703 | 2 |
| #23778692 | 2 |
| #103×C317 | 2 |
| #448 | 317 |