Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C163 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C163 |
| prime radical | #525×C163 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×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. #485×C163 | C2 | semidirect |
| 4. #482×C163 | C2 | semidirect |
| 5. #428×C163 | C2 | semidirect |
| 6. #417×C163 | C2 | semidirect |
| 7. #407×C163 | C2 | semidirect |
| 22. #107×C163 | C22 | semidirect |
| 23. #106×C163 | C22 | semidirect |
| 24. #103×C163 | C22 | semidirect |
| 25. #102×C163 | C22 | semidirect |
| 94. C163 | #3093 | direct (N × H) |
| 95. #3093 | C163 | direct (N × H) |
| 97. C2×#117 | C2×C163 | semidirect |
| 98. #485 | C2×C163 | semidirect |
| 99. #482 | C2×C163 | semidirect |
| 100. #428 | C2×C163 | semidirect |
| 101. #417 | C2×C163 | semidirect |
| 102. #407 | C2×C163 | semidirect |
| 117. #107 | C22×C163 | semidirect |
| 118. #106 | C22×C163 | semidirect |
| 119. #103 | C22×C163 | semidirect |
| 120. #102 | C22×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 |
| #485×C163 | 2 |
| #482×C163 | 2 |
| #428×C163 | 2 |
| #417×C163 | 2 |
| #407×C163 | 2 |
| #3093 | 163 |