Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
234 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4×#14579683 | C2 | semidirect |
| 2. C2×#19104646 | C2 | semidirect |
| 3. #23781407 | C2 | semidirect |
| 4. #23781405 | C2 | semidirect |
| 91. C163 | #1524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579683 | 2 |
| C2×#19104646 | 2 |
| #23781407 | 2 |
| #23781405 | 2 |
| #529×C163 | 2 |
| #1524 | 163 |