Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 1. C8×Dic326 | C2 | semidirect |
| 3. #23781415 | C2 | semidirect |
| 4. #23781395 | C2 | semidirect |
| 6. C8×C163⋊C8 | C2 | semidirect |
| 24. #14579687 | C8 | direct (N × H) |
| 42. Dic326 | C2×C8 | semidirect |
| 48. C163⋊C8 | C2×C8 | semidirect |
| 60. C8×C163 | SD16 | semidirect |
| 77. C163 | C8×SD16 | semidirect |
| 138. C8 | #14579687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic326 | 2 |
| C4×#14579687 | 2 |
| #23781415 | 2 |
| #23781395 | 2 |
| D4⋊(C163⋊C8) | 2 |
| C8×C163⋊C8 | 2 |
| C8×D4×C163 | 2 |
| C8×SD16 | 163 |