Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C163 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C163 |
| prime radical | #576×C163 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C163 ◁ C2×C4×C163 ◁ #131×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #510×C163 | C2 | semidirect |
| 3. C2×SD32×C163 | C2 | semidirect |
| 4. #473×C163 | C2 | semidirect |
| 5. #361×C163 | C2 | semidirect |
| 6. #359×C163 | C2 | semidirect |
| 7. #350×C163 | C2 | semidirect |
| 14. C2×Q16×C163 | C22 | semidirect |
| 21. M32×C163 | C22 | semidirect |
| 22. C2×C16×C163 | C22 | semidirect |
| 23. #108×C163 | C22 | semidirect |
| 91. C163 | #2194 | direct (N × H) |
| 92. #2194 | C163 | direct (N × H) |
| 94. #510 | C2×C163 | semidirect |
| 95. C2×SD32 | C2×C163 | semidirect |
| 96. #473 | C2×C163 | semidirect |
| 97. #361 | C2×C163 | semidirect |
| 98. #359 | C2×C163 | semidirect |
| 99. #350 | C2×C163 | semidirect |
| 106. C2×Q16 | C22×C163 | semidirect |
| 113. M32 | C22×C163 | semidirect |
| 114. C2×C16 | C22×C163 | semidirect |
| 115. #108 | C22×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #576×C163 | 2 |
| #510×C163 | 2 |
| C2×SD32×C163 | 2 |
| #473×C163 | 2 |
| #361×C163 | 2 |
| #359×C163 | 2 |
| #350×C163 | 2 |
| #2194 | 163 |