Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
228 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C163 | D8 |
| commutator | C8 | C22×C4×C163 |
| Frattini, cosocle | C2×C8 | C23×C163 |
| socle | C22×C163 | C2×D8 |
| prime radical | C2×#135×C163 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×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. C22×C16×C163 | C2 | semidirect |
| 3. #427×C163 | C2 | semidirect |
| 4. #358×C163 | C2 | semidirect |
| 5. #357×C163 | C2 | semidirect |
| 8. #135×C163 | C4 | semidirect |
| 69. C163 | #2138 | direct (N × H) |
| 70. #2138 | C163 | direct (N × H) |
| 72. C22×C16 | C2×C163 | semidirect |
| 73. #427 | C2×C163 | semidirect |
| 74. #358 | C2×C163 | semidirect |
| 75. #357 | C2×C163 | semidirect |
| 78. #135 | C4×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 |
| C22×C16×C163 | 2 |
| #427×C163 | 2 |
| #358×C163 | 2 |
| #357×C163 | 2 |
| #2138 | 163 |