Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
406 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C163 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C163 ◁ C22×C4×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 2. #537×C163 | C2 | semidirect |
| 3. C2×#104×C163 | C2 | semidirect |
| 4. #390×C163 | C2 | semidirect |
| 5. #343×C163 | C2 | semidirect |
| 32. C2×D4×C163 | D4 | semidirect |
| 40. M16×C163 | D4 | semidirect |
| 101. C163 | #2006 | direct (N × H) |
| 102. #2006 | C163 | direct (N × H) |
| 103. C2×AGL(1,ℤ/8) | C2×C163 | semidirect |
| 104. #537 | C2×C163 | semidirect |
| 105. C2×#104 | C2×C163 | semidirect |
| 106. #390 | C2×C163 | semidirect |
| 107. #343 | C2×C163 | semidirect |
| 134. C2×D4 | D4×C163 | semidirect |
| 142. M16 | D4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #537×C163 | 2 |
| C2×#104×C163 | 2 |
| #390×C163 | 2 |
| #343×C163 | 2 |
| #2006 | 163 |