Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 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×D652 | C2 | semidirect |
| 2. #23782012 | C2 | semidirect |
| 3. #23781865 | C2 | semidirect |
| 5. #23781410 | C2 | semidirect |
| 6. #23781394 | C2 | semidirect |
| 7. Q8⋊C8×C163 | C2 | semidirect |
| 62. D652 | SD16 | semidirect |
| 70. Q8×C163 | D8 | semidirect |
| 99. C163 | #1627 | semidirect |
| 106. Q8⋊C8 | D163 | semidirect |
| 157. Q8 | D1304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D652 | 2 |
| #23782012 | 2 |
| #23781865 | 2 |
| #23781861 | 2 |
| #23781410 | 2 |
| #23781394 | 2 |
| Q8⋊C8×C163 | 2 |
| #1627 | 163 |