Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#19104676 | C2 | semidirect |
| 2. C22×C163⋊C16 | C2 | semidirect |
| 3. #23781901 | C2 | semidirect |
| 4. #23781490 | C2 | semidirect |
| 5. #23781466 | C2 | semidirect |
| 6. #23781465 | C2 | semidirect |
| 7. #466×C163 | C2 | semidirect |
| 28. C163⋊C16 | D4 | semidirect |
| 63. C22×C163 | D16 | semidirect |
| 79. C163 | #2215 | semidirect |
| 84. #466 | D163 | semidirect |
| 146. C22 | #19104676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104676 | 2 |
| C22×C163⋊C16 | 2 |
| #23781901 | 2 |
| #23781490 | 2 |
| #23781466 | 2 |
| #23781465 | 2 |
| #466×C163 | 2 |
| #2215 | 163 |