Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #23781402 | C2 | semidirect |
| 11. C22×Q8×C163 | C4 | semidirect |
| 15. C22⋊Q8×C163 | C4 | semidirect |
| 18. C2×C4⋊C4×C163 | C4 | semidirect |
| 93. C163 | #1511 | semidirect |
| 99. C22×Q8 | Dic163 | semidirect |
| 104. C22⋊Q8 | Dic163 | semidirect |
| 107. C2×C4⋊C4 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781629 | 2 |
| #23781528 | 2 |
| #23781402 | 2 |
| C2×C22⋊Q8×C163 | 2 |
| #1511 | 163 |