Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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 |
|---|---|---|
| 2. #23781409 | C2 | semidirect |
| 3. #353×C163 | C2 | semidirect |
| 4. #19104780 | C4 | semidirect |
| 8. #19104652 | C4 | semidirect |
| 59. C163 | #1402 | semidirect |
| 62. #353 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781832 | 2 |
| #23781409 | 2 |
| #353×C163 | 2 |
| #1402 | 163 |