Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
270 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C2×#99 |
| commutator | C2×C4 | C22×C4×C163 |
| Frattini, cosocle | C2×D4 | C23×C163 |
| prime radical | #535×C163 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C163 ◁ C2×C4×C163 ◁ C2×#41×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #410×C163 | C2 | semidirect |
| 3. #353×C163 | C2 | semidirect |
| 5. C22×D4×C163 | C4 | semidirect |
| 7. #124×C163 | C4 | semidirect |
| 11. #117×C163 | C4 | semidirect |
| 13. #99×C163 | C22 | semidirect |
| 69. C163 | #2128 | direct (N × H) |
| 70. #2128 | C163 | direct (N × H) |
| 72. #410 | C2×C163 | semidirect |
| 73. #353 | C2×C163 | semidirect |
| 75. C22×D4 | C4×C163 | semidirect |
| 77. #124 | C4×C163 | semidirect |
| 81. #117 | C4×C163 | semidirect |
| 83. #99 | C22×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #535×C163 | 2 |
| #410×C163 | 2 |
| #353×C163 | 2 |
| #2128 | 163 |