Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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 | #394×C163 | C2 |
| prime radical | C22×#14579698 | C2 |
| hypercenter | #394 | D163 |
| hypocenter | C163 | #2406 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#19104717 | C2 | semidirect |
| 3. C2×C4⋊C4×D163 | C2 | semidirect |
| 4. #23781586 | C2 | semidirect |
| 5. #23781585 | C2 | semidirect |
| 6. #23781579 | C2 | semidirect |
| 7. #23781541 | C2 | semidirect |
| 8. #23781540 | C2 | semidirect |
| 9. #23781537 | C2 | semidirect |
| 10. #23781527 | C2 | semidirect |
| 11. #394×C163 | C2 | semidirect |
| 99. C2×Dic163 | #41 | semidirect |
| 121. C2×C4×C163 | #41 | semidirect |
| 155. C163 | #2406 | semidirect |
| 163. #394 | D163 | semidirect |
| 277. C2×C4 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C2×#19104717 | 2 |
| C2×C4⋊C4×D163 | 2 |
| #23781586 | 2 |
| #23781585 | 2 |
| #23781579 | 2 |
| #23781541 | 2 |
| #23781540 | 2 |
| #23781537 | 2 |
| #23781527 | 2 |
| #394×C163 | 2 |
| #2406 | 163 |