Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 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, prime radical | C22×#41×C163 | C2 |
| hypercenter | C22×#41 | D163 |
| hypocenter | C163 | #2432 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104733 | C2 | semidirect |
| 2. C2×#19104722 | C2 | semidirect |
| 3. C2×#19104714 | C2 | semidirect |
| 4. #23781579 | C2 | semidirect |
| 5. #23781572 | C2 | semidirect |
| 6. #23781568 | C2 | semidirect |
| 7. #23781538 | C2 | semidirect |
| 8. C4×C22⋊Dic163 | C2 | semidirect |
| 81. C2×Dic163 | #41 | semidirect |
| 136. C163 | #2432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104733 | 2 |
| C2×#19104722 | 2 |
| C2×#19104714 | 2 |
| #23781579 | 2 |
| #23781572 | 2 |
| #23781568 | 2 |
| #23781538 | 2 |
| C4×C22⋊Dic163 | 2 |
| C22×#41×C163 | 2 |
| #2432 | 163 |