Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19104718 | C2 | semidirect |
| 3. C2×#19104650 | C2 | semidirect |
| 4. C2×#19104649 | C2 | semidirect |
| 5. #23781528 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. C2×#123×C163 | C2 | semidirect |
| 51. C22⋊Dic163 | D4 | semidirect |
| 70. C22×C4×C163 | D4 | semidirect |
| 74. C22⋊C4×C163 | D4 | semidirect |
| 160. C163 | #2022 | semidirect |
| 164. C2×#123 | D163 | semidirect |
| 220. C22×C4 | C22⋊D163 | semidirect |
| 235. C22⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782224 | 2 |
| C2×#19104718 | 2 |
| C2×#19104650 | 2 |
| C2×#19104649 | 2 |
| #23781528 | 2 |
| #23781431 | 2 |
| C2×#123×C163 | 2 |
| #2022 | 163 |