Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23781716 | C2 | semidirect |
| 3. #23781687 | C2 | semidirect |
| 4. #23781394 | C2 | semidirect |
| 5. D4⋊(C163⋊C8) | C2 | semidirect |
| 6. #23781392 | C2 | semidirect |
| 7. D4⋊C8×C163 | C2 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. C4×C163⋊C8 | C22 | semidirect |
| 25. C4⋊C8×C163 | C22 | semidirect |
| 26. C4×C8×C163 | C22 | semidirect |
| 65. D652 | M16 | semidirect |
| 85. D4×C163 | M16 | semidirect |
| 121. C163 | #1486 | semidirect |
| 129. D4⋊C8 | D163 | semidirect |
| 145. C4⋊C8 | C2×D163 | semidirect |
| 148. C4×C8 | C2×D163 | semidirect |
| 191. D4 | #14579682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D163 | 2 |
| #23781716 | 2 |
| #23781687 | 2 |
| #23781394 | 2 |
| D4⋊(C163⋊C8) | 2 |
| #23781392 | 2 |
| D4⋊C8×C163 | 2 |
| #1486 | 163 |