Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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×#19104650 | C2 | semidirect |
| 3. C2×#19104649 | C2 | semidirect |
| 4. C2×#19104649 | C2 | semidirect |
| 5. #23781523 | C2 | semidirect |
| 6. C22⋊C4×Dic163 | C2 | semidirect |
| 7. C2×#99×C163 | C2 | semidirect |
| 8. C22×C22⋊D163 | C4 | semidirect |
| 16. C2×Dic163⋊C4 | C4 | semidirect |
| 17. C2×C22⋊Dic163 | C4 | semidirect |
| 20. C2×(C2×D163)⋊C4 | C4 | semidirect |
| 59. C22⋊Dic163 | D4 | semidirect |
| 77. C22⋊C4×C163 | D4 | semidirect |
| 171. Dic163 | #99 | semidirect |
| 183. C163 | #1964 | semidirect |
| 189. C2×#99 | D163 | semidirect |
| 260. C22⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104707 | 2 |
| C2×#19104650 | 2 |
| C2×#19104649 | 2 |
| #23781523 | 2 |
| C22⋊C4×Dic163 | 2 |
| C2×#99×C163 | 2 |
| #1964 | 163 |