Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782215 | C2 | semidirect |
| 2. #23782068 | C2 | semidirect |
| 3. #23782041 | C2 | semidirect |
| 4. #23782013 | C2 | semidirect |
| 5. #23782011 | C2 | semidirect |
| 6. #23781899 | C2 | semidirect |
| 7. C4×#14579684 | C2 | semidirect |
| 8. C2×C4×C163⋊C8 | C2 | semidirect |
| 9. #532×C163 | C2 | semidirect |
| 77. C163⋊C8 | #41 | semidirect |
| 89. C2×C4×C163 | D8 | semidirect |
| 120. C163 | #3169 | semidirect |
| 123. #532 | D163 | semidirect |
| 208. C2×C4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| #23782068 | 2 |
| #23782041 | 2 |
| #23782013 | 2 |
| #23782011 | 2 |
| #23781899 | 2 |
| C4×#14579684 | 2 |
| C2×C4×C163⋊C8 | 2 |
| #532×C163 | 2 |
| #3169 | 163 |