Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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×C8×D317 | C2 | semidirect |
| 2. #23778756 | C2 | semidirect |
| 4. #23778712 | C2 | semidirect |
| 5. #23778704 | C2 | semidirect |
| 6. #23778701 | C2 | semidirect |
| 7. C2×SD16×C317 | C2 | semidirect |
| 36. C8×C317 | D4 | semidirect |
| 43. C2×D317 | SD16 | semidirect |
| 55. C317 | #465 | semidirect |
| 57. C2×SD16 | D317 | semidirect |
| 92. C8 | C22⋊D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D317 | 2 |
| #23778756 | 2 |
| #23778751 | 2 |
| #23778712 | 2 |
| #23778704 | 2 |
| #23778701 | 2 |
| C2×SD16×C317 | 2 |
| #465 | 317 |