Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23782061 | C2 | semidirect |
| 4. #23782015 | C2 | semidirect |
| 6. #23781386 | C2 | semidirect |
| 7. #500×C163 | C2 | semidirect |
| 54. C8×C163 | SD16 | semidirect |
| 69. C163 | #1714 | semidirect |
| 71. #500 | D163 | semidirect |
| 124. C8 | #14579686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782061 | 2 |
| #23782039 | 2 |
| #23782038 | 2 |
| #23782015 | 2 |
| #23782013 | 2 |
| #23781386 | 2 |
| #500×C163 | 2 |
| #1714 | 163 |