Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1462 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1462 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator | C23×C79 | C23×C4 |
| Fitting | C79×#1446 | C2 |
| socle, prime radical, cosocle | C24×C79 | C24 |
| hypercenter | #1446 | D79 |
| hypocenter | C79 | #14663 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ #1446 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×#14579159 | C4 | semidirect |
| 140. C79 | #14663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579159 | 2 |
| C2×#19098430 | 2 |
| #23761671 | 2 |
| #23761670 | 2 |
| #23761666 | 2 |
| C79×#1446 | 2 |
| #14663 | 79 |