Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
220 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C163 | C2×D8 |
| commutator | C8 | C22×C4×C163 |
| Frattini, cosocle | C2×C8 | C23×C163 |
| socle | C2×C163 | C2×#102 |
| prime radical | C2×#135×C163 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C163 ◁ C22×C4×C163 ◁ C22×C8×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×M32×C163 | C2 | semidirect |
| 3. C2×#108×C163 | C2 | semidirect |
| 4. #359×C163 | C2 | semidirect |
| 17. C2×C16×C163 | C22 | semidirect |
| 19. #108×C163 | C22 | semidirect |
| 83. C163 | #2143 | direct (N × H) |
| 84. #2143 | C163 | direct (N × H) |
| 86. C2×M32 | C2×C163 | semidirect |
| 87. C2×#108 | C2×C163 | semidirect |
| 88. #359 | C2×C163 | semidirect |
| 101. C2×C16 | C22×C163 | semidirect |
| 103. #108 | C22×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135×C163 | 2 |
| C2×M32×C163 | 2 |
| C2×#108×C163 | 2 |
| #359×C163 | 2 |
| #2143 | 163 |