Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
358 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C163 | C2×D4 |
| commutator | C2×C4 | C22×C4×C163 |
| Frattini, cosocle | C22×C4 | C23×C163 |
| socle | C22×C163 | C2×C22⋊C4 |
| prime radical | #525×C163 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C163 ◁ C23×C4×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#117×C163 | C2 | semidirect |
| 3. C2×#104×C163 | C2 | semidirect |
| 4. #407×C163 | C2 | semidirect |
| 5. #339×C163 | C2 | semidirect |
| 10. C22⋊Q8×C163 | C4 | semidirect |
| 11. #121×C163 | C4 | semidirect |
| 48. C42×C163 | D4 | semidirect |
| 98. C163 | #1897 | direct (N × H) |
| 99. #1897 | C163 | direct (N × H) |
| 101. C2×#117 | C2×C163 | semidirect |
| 102. C2×#104 | C2×C163 | semidirect |
| 103. #407 | C2×C163 | semidirect |
| 104. #339 | C2×C163 | semidirect |
| 109. C22⋊Q8 | C4×C163 | semidirect |
| 110. #121 | C4×C163 | semidirect |
| 147. C42 | D4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #525×C163 | 2 |
| C2×#117×C163 | 2 |
| C2×#104×C163 | 2 |
| #407×C163 | 2 |
| #339×C163 | 2 |
| #1897 | 163 |