Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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, socle, cosocle | C23×C163 | C24 |
| Fitting | #381×C163 | C2 |
| prime radical | C22×C22⋊D163 | C22 |
| hypercenter | #381 | D163 |
| hypocenter | C163 | #2853 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×Dic163 | C2 | semidirect |
| 3. #23781557 | C2 | semidirect |
| 4. #23781550 | C2 | semidirect |
| 6. #23781540 | C2 | semidirect |
| 7. #381×C163 | C2 | semidirect |
| 84. C163 | #2853 | semidirect |
| 92. #381 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104718 | 2 |
| C22×C4×Dic163 | 2 |
| #23781557 | 2 |
| #23781550 | 2 |
| #23781542 | 2 |
| #23781540 | 2 |
| #381×C163 | 2 |
| #2853 | 163 |