Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic317 | C2 | semidirect |
| 3. #23778712 | C2 | semidirect |
| 4. #23778704 | C2 | semidirect |
| 6. C8×Dic317 | C2 | semidirect |
| 18. SD16×C317 | C4 | semidirect |
| 28. Q8×C317 | C2×C4 | semidirect |
| 33. C8×C317 | C2×C4 | semidirect |
| 44. Dic317 | SD16 | direct (N × H) |
| 49. C317 | C4×SD16 | semidirect |
| 61. SD16 | Dic317 | direct (N × H) |
| 72. Q8 | C2×Dic317 | semidirect |
| 83. C8 | C2×Dic317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic317 | 2 |
| D4×Dic317 | 2 |
| #23778712 | 2 |
| #23778704 | 2 |
| #23778701 | 2 |
| C8×Dic317 | 2 |
| C2×SD16×C317 | 2 |
| C4×SD16 | 317 |