Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#19104680 | C2 | semidirect |
| 2. C2×#19104679 | C2 | semidirect |
| 3. C2×#19104676 | C2 | semidirect |
| 4. #23782048 | C2 | semidirect |
| 5. #23782040 | C2 | semidirect |
| 6. #23781440 | C2 | semidirect |
| 7. C2×D16×C163 | C2 | semidirect |
| 35. C163⋊C16 | D4 | semidirect |
| 43. C16×C163 | D4 | semidirect |
| 78. C163 | #2250 | semidirect |
| 83. C2×D16 | D163 | semidirect |
| 122. C16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104680 | 2 |
| C2×#19104679 | 2 |
| C2×#19104676 | 2 |
| #23782048 | 2 |
| #23782040 | 2 |
| #23781440 | 2 |
| C2×D16×C163 | 2 |
| #2250 | 163 |