Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 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×#19104724 | C2 | semidirect |
| 3. #23781576 | C2 | semidirect |
| 4. #23781572 | C2 | semidirect |
| 5. #23781544 | C2 | semidirect |
| 6. C4×C22⋊Dic163 | C2 | semidirect |
| 7. C23×Q8×C163 | C2 | semidirect |
| 43. C2×Q8×C163 | D4 | semidirect |
| 81. C22×C163 | #124 | semidirect |
| 101. C163 | #2436 | semidirect |
| 103. C23×Q8 | D163 | semidirect |
| 134. C2×Q8 | C22⋊D163 | semidirect |
| 187. C22 | #19104724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104724 | 2 |
| C2×#19104709 | 2 |
| #23781576 | 2 |
| #23781572 | 2 |
| #23781544 | 2 |
| C4×C22⋊Dic163 | 2 |
| C23×Q8×C163 | 2 |
| #2436 | 163 |