Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19104756 | C2 | semidirect |
| 2. #23782216 | C2 | semidirect |
| 3. C4×#14579698 | C2 | semidirect |
| 4. #23781890 | C2 | semidirect |
| 5. #23781882 | C2 | semidirect |
| 6. #23781872 | C2 | semidirect |
| 7. #23781866 | C2 | semidirect |
| 8. #23781860 | C2 | semidirect |
| 9. C4⋊C8×D163 | C2 | semidirect |
| 10. #23781660 | C2 | semidirect |
| 11. #461×C163 | C2 | semidirect |
| 47. #14579698 | D4 | semidirect |
| 136. C4×C163 | #135 | semidirect |
| 150. C163 | #3035 | semidirect |
| 158. #461 | D163 | semidirect |
| 292. C4 | #19104756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104756 | 2 |
| #23782216 | 2 |
| C4×#14579698 | 2 |
| #23781890 | 2 |
| #23781882 | 2 |
| #23781872 | 2 |
| #23781866 | 2 |
| #23781860 | 2 |
| C4⋊C8×D163 | 2 |
| #23781660 | 2 |
| #461×C163 | 2 |
| #3035 | 163 |