Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 108 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 | #386 |
| commutator | C2×C4 | C22×C4×C163 |
| Frattini, cosocle | C22×C4 | C23×C163 |
| prime radical | #535×C163 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C163 ◁ C22×C4×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #518×C163 | C2 | semidirect |
| 3. #421×C163 | C2 | semidirect |
| 4. C2×#100×C163 | C2 | semidirect |
| 5. H(3,ℤ/4)×C163 | C2 | semidirect |
| 9. #127×C163 | C4 | semidirect |
| 10. #124×C163 | C4 | semidirect |
| 22. C2×Q8×C163 | C2×C4 | semidirect |
| 28. C2×D4×C163 | C2×C4 | semidirect |
| 42. C42×C163 | C2×C4 | semidirect |
| 43. C42×C163 | D4 | semidirect |
| 88. C163 | #1911 | direct (N × H) |
| 89. #1911 | C163 | direct (N × H) |
| 91. #518 | C2×C163 | semidirect |
| 92. #421 | C2×C163 | semidirect |
| 93. C2×#100 | C2×C163 | semidirect |
| 94. H(3,ℤ/4) | C2×C163 | semidirect |
| 98. #127 | C4×C163 | semidirect |
| 99. #124 | C4×C163 | semidirect |
| 111. C2×Q8 | C2×C4×C163 | semidirect |
| 117. C2×D4 | C2×C4×C163 | semidirect |
| 131. C42 | C2×C4×C163 | semidirect |
| 132. C42 | D4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #535×C163 | 2 |
| #518×C163 | 2 |
| #421×C163 | 2 |
| C2×#100×C163 | 2 |
| H(3,ℤ/4)×C163 | 2 |
| #1911 | 163 |