Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | C2×#354 |
| commutator | C42 | C22×C4×C79 |
| Frattini, cosocle | #127 | C23×C79 |
| prime radical | #532×C79 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×C4×C79 ◁ C22×C4×C79 ◁ #532×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C79×#1412 | C2 | semidirect |
| 5. C2×#125×C79 | C4 | semidirect |
| 6. #491×C79 | C4 | semidirect |
| 11. C4×M16×C79 | C4 | semidirect |
| 89. #13596 | C79 | direct (N × H) |
| 96. #1412 | C2×C79 | semidirect |
| 97. C79 | #13596 | direct (N × H) |
| 99. C2×#125 | C4×C79 | semidirect |
| 100. #491 | C4×C79 | semidirect |
| 105. C4×M16 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3142 | 2 |
| C79×#2126 | 2 |
| C79×#1412 | 2 |
| #13596 | 79 |