Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1718 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1718 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C79 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C79 |
| Frattini, cosocle | C2×C42 | C23×C79 |
| prime radical | C22×#127×C79 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ C22×C42×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#1797 | C2 | semidirect |
| 3. C2×#331×C79 | C2 | semidirect |
| 11. C2×C4⋊C8×C79 | C22 | semidirect |
| 130. C22×C79 | #331 | semidirect |
| 141. #8339 | C79 | direct (N × H) |
| 150. #1797 | C2×C79 | semidirect |
| 151. C2×#331 | C2×C79 | semidirect |
| 152. C79 | #8339 | direct (N × H) |
| 160. C2×C4⋊C8 | C22×C79 | semidirect |
| 279. C22 | #331×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#127×C79 | 2 |
| C79×#1797 | 2 |
| C2×#331×C79 | 2 |
| #8339 | 79 |