Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23782432 | C2 | semidirect |
| 2. #23781682 | C2 | semidirect |
| 3. #23781639 | C2 | semidirect |
| 4. #23781425 | C2 | semidirect |
| 14. C4⋊Q8×C163 | C4 | semidirect |
| 15. #127×C163 | C4 | semidirect |
| 16. #124×C163 | C4 | semidirect |
| 17. #124×C163 | C4 | semidirect |
| 23. #14579683 | D4 | semidirect |
| 95. C163 | #1884 | semidirect |
| 107. C4⋊Q8 | Dic163 | semidirect |
| 108. #127 | Dic163 | semidirect |
| 109. #124 | Dic163 | semidirect |
| 110. #124 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782432 | 2 |
| #23781682 | 2 |
| #23781639 | 2 |
| #23781425 | 2 |
| #532×C163 | 2 |
| #1884 | 163 |