Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
410 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 176 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C163 |
| prime radical | C24×C163 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C163 ◁ C23×C4×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #483×C163 | C2 | semidirect |
| 3. #470×C163 | C2 | semidirect |
| 4. #451×C163 | C2 | semidirect |
| 8. C2×Q16×C163 | C22 | semidirect |
| 17. #106×C163 | C22 | semidirect |
| 18. #103×C163 | C22 | semidirect |
| 74. C163 | #3195 | direct (N × H) |
| 75. #3195 | C163 | direct (N × H) |
| 77. #483 | C2×C163 | semidirect |
| 78. #470 | C2×C163 | semidirect |
| 79. #451 | C2×C163 | semidirect |
| 83. C2×Q16 | C22×C163 | semidirect |
| 92. #106 | C22×C163 | semidirect |
| 93. #103 | C22×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C163 | 2 |
| #483×C163 | 2 |
| #470×C163 | 2 |
| #451×C163 | 2 |
| #407×C163 | 2 |
| #3195 | 163 |