Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 2. #23782038 | C2 | semidirect |
| 3. #23781956 | C2 | semidirect |
| 4. #23781955 | C2 | semidirect |
| 5. #23781408 | C2 | semidirect |
| 6. #23781394 | C2 | semidirect |
| 7. D4⋊C8×C163 | C2 | semidirect |
| 11. #19104735 | C22 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. C4⋊C8×C163 | C22 | semidirect |
| 24. C4×C8×C163 | C22 | semidirect |
| 65. D652 | SD16 | semidirect |
| 74. D4×C163 | SD16 | semidirect |
| 108. C163 | #1629 | semidirect |
| 116. D4⋊C8 | D163 | semidirect |
| 130. C4⋊C8 | C2×D163 | semidirect |
| 133. C4×C8 | C2×D163 | semidirect |
| 178. D4 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D652 | 2 |
| #23782038 | 2 |
| #23781956 | 2 |
| #23781955 | 2 |
| #23781408 | 2 |
| #23781394 | 2 |
| D4⋊C8×C163 | 2 |
| #1629 | 163 |