Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
168 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #23781415 | C2 | semidirect |
| 4. Q8⋊(C163⋊C8) | C2 | semidirect |
| 6. #23781386 | C2 | semidirect |
| 7. #446×C163 | C2 | semidirect |
| 60. C8×C163 | SD16 | semidirect |
| 77. C163 | #1582 | semidirect |
| 79. #446 | D163 | semidirect |
| 138. C8 | #14579686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579686 | 2 |
| C8×D652 | 2 |
| #23781415 | 2 |
| Q8⋊(C163⋊C8) | 2 |
| #23781392 | 2 |
| #23781386 | 2 |
| #446×C163 | 2 |
| #1582 | 163 |