Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23782222 | C2 | semidirect |
| 3. #23782063 | C2 | semidirect |
| 4. #23782038 | C2 | semidirect |
| 5. #23782016 | C2 | semidirect |
| 6. #23782012 | C2 | semidirect |
| 7. #23781894 | C2 | semidirect |
| 8. C4×#14579688 | C2 | semidirect |
| 9. C2×C4×C8×C163 | C2 | semidirect |
| 82. C2×C4×C163 | SD16 | semidirect |
| 90. C8×C163 | #41 | semidirect |
| 112. C163 | #3167 | semidirect |
| 122. C2×C4×C8 | D163 | semidirect |
| 195. C2×C4 | #14579688 | semidirect |
| 203. C8 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23782215 | 2 |
| #23782063 | 2 |
| #23782038 | 2 |
| #23782016 | 2 |
| #23782012 | 2 |
| #23781894 | 2 |
| C4×#14579688 | 2 |
| C2×C4×C8×C163 | 2 |
| #3167 | 163 |