Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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. D317⋊M16 | C2 | semidirect |
| 2. #23778859 | C2 | semidirect |
| 3. #23778842 | C2 | semidirect |
| 7. D317⋊C8 | C22 | semidirect |
| 8. C4⋊#11929639 | C22 | semidirect |
| 12. C2×D1268 | C4 | semidirect |
| 16. D4×D317 | C4 | semidirect |
| 19. C2×D4×C317 | C4 | semidirect |
| 61. C317 | #418 | semidirect |
| 74. C2×D4 | #11929639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D317⋊M16 | 2 |
| #23778859 | 2 |
| #23778842 | 2 |
| C2×D4×D317 | 2 |
| #418 | 317 |