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 |
|---|---|---|
| 1. C2×#19104668 | C2 | semidirect |
| 2. C2×#19104666 | C2 | semidirect |
| 5. #23781427 | C2 | semidirect |
| 6. #23781427 | C2 | semidirect |
| 15. C22⋊(C163⋊C8) | C4 | semidirect |
| 120. C163 | #1854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104668 | 2 |
| C2×#19104666 | 2 |
| C2×C22⋊(C163⋊C8) | 2 |
| #23781525 | 2 |
| #23781427 | 2 |
| C2×#117×C163 | 2 |
| #1854 | 163 |