Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
800 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 193 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. C2×#19104733 | C2 | semidirect |
| 4. #23781585 | C2 | semidirect |
| 5. #23781572 | C2 | semidirect |
| 6. #23781571 | C2 | semidirect |
| 9. C2×C4⋊Q8×C163 | C2 | semidirect |
| 55. (C2×D163)⋊C4 | Q8 | semidirect |
| 86. C2×Dic163 | C2×Q8 | semidirect |
| 103. C2×C4×C163 | C2×Q8 | semidirect |
| 113. C2×D163 | C4⋊Q8 | semidirect |
| 128. C163 | #2434 | semidirect |
| 132. C2×C4⋊Q8 | D163 | semidirect |
| 232. C2×C4 | Q8×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D163 | 2 |
| C2×#19104733 | 2 |
| C2×#19104711 | 2 |
| #23781585 | 2 |
| #23781572 | 2 |
| #23781571 | 2 |
| #23781536 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C2×C4⋊Q8×C163 | 2 |
| #2434 | 163 |