Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782414 | C2 | semidirect |
| 2. #23781848 | C2 | semidirect |
| 4. #23781464 | C2 | semidirect |
| 5. #23781463 | C2 | semidirect |
| 6. #23781461 | C2 | semidirect |
| 7. #456×C163 | C2 | semidirect |
| 106. C163 | #2203 | semidirect |
| 110. #456 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782414 | 2 |
| #23781848 | 2 |
| #23781838 | 2 |
| #23781464 | 2 |
| #23781463 | 2 |
| #23781461 | 2 |
| #456×C163 | 2 |
| #2203 | 163 |