Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#19104741 | C2 | semidirect |
| 3. #23781744 | C2 | semidirect |
| 4. C8×D652 | C2 | semidirect |
| 5. #23781689 | C2 | semidirect |
| 6. #23781631 | C2 | semidirect |
| 7. C2×C4×C8×C163 | C2 | semidirect |
| 41. C2×C8×C163 | D4 | semidirect |
| 75. C4×C163 | #131 | semidirect |
| 83. C163 | #2931 | semidirect |
| 91. C2×C4×C8 | D163 | semidirect |
| 123. C2×C8 | D652 | semidirect |
| 160. C4 | #19104741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104741 | 2 |
| #23782215 | 2 |
| #23781744 | 2 |
| C8×D652 | 2 |
| #23781689 | 2 |
| #23781631 | 2 |
| C2×C4×C8×C163 | 2 |
| #2931 | 163 |