Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
526 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C79 |
| prime radical | C22×D4×C79 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#3249 | C2 | semidirect |
| 4. C79×#1493 | C2 | semidirect |
| 5. C79×#1292 | C2 | semidirect |
| 57. C2×D4×C79 | Q16 | semidirect |
| 137. #10258 | C79 | direct (N × H) |
| 144. #3249 | C2×C79 | semidirect |
| 147. #1493 | C2×C79 | semidirect |
| 148. #1292 | C2×C79 | semidirect |
| 149. C79 | #10258 | direct (N × H) |
| 201. C2×D4 | Q16×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3249 | 2 |
| C79×#3077 | 2 |
| C79×#1954 | 2 |
| C79×#1493 | 2 |
| C79×#1292 | 2 |
| #10258 | 79 |