Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
316 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19104668 | C2 | semidirect |
| 3. C2×#19104666 | C2 | semidirect |
| 5. #23781427 | C2 | semidirect |
| 6. #23781427 | C2 | semidirect |
| 10. C2×#14579683 | C4 | semidirect |
| 61. C163⋊C8 | C22⋊C4 | semidirect |
| 120. C163 | #1809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579683 | 2 |
| C2×#19104668 | 2 |
| C2×#19104666 | 2 |
| #23781525 | 2 |
| #23781427 | 2 |
| #380×C163 | 2 |
| #1809 | 163 |