Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
620 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104662 | C2 | semidirect |
| 2. #23781666 | C2 | semidirect |
| 3. C2×#19104652 | C2 | semidirect |
| 4. #23781568 | C2 | semidirect |
| 6. C2×#14579683 | C22 | semidirect |
| 7. C2×C4⋊Dic163 | C22 | semidirect |
| 9. C2×C4×Dic163 | C22 | semidirect |
| 16. H(5,𝔽2)×C163 | C4 | semidirect |
| 70. Q8×C163 | C22⋊C4 | semidirect |
| 77. D4×C163 | C22⋊C4 | semidirect |
| 112. C163 | #1792 | semidirect |
| 121. H(5,𝔽2) | Dic163 | semidirect |
| 177. Q8 | C22⋊Dic163 | semidirect |
| 184. D4 | C22⋊Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104662 | 2 |
| #23781666 | 2 |
| C2×#19104652 | 2 |
| #23781568 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| #1792 | 163 |