Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
464 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 193 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D163 |
| commutator | C22×C163 | C23×C4 |
| Fitting | #382×C163 | C2 |
| socle, prime radical, cosocle | C23×C163 | C24 |
| hypercenter | #382 | D163 |
| hypocenter | C163 | #2356 |
| LCS | G ▷ C22×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×Dic326 | C4 | semidirect |
| 86. C163 | #2356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic326 | 2 |
| #23781570 | 2 |
| #23781552 | 2 |
| #23781532 | 2 |
| C4⋊C4×Dic163 | 2 |
| C4×C4⋊Dic163 | 2 |
| #23781510 | 2 |
| #382×C163 | 2 |
| #2356 | 163 |