Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
178 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #23781387 | C2 | semidirect |
| 4. #23781387 | C2 | semidirect |
| 5. #23781386 | C2 | semidirect |
| 6. C8×C163⋊C8 | C2 | semidirect |
| 64. C163 | #1454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781718 | 2 |
| #23781387 | 2 |
| #23781386 | 2 |
| C8×C163⋊C8 | 2 |
| #431×C163 | 2 |
| #1454 | 163 |