Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C79 |
| prime radical | C79×#3191 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ C2×C22⋊C8×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C79×#2188 | C2 | semidirect |
| 3. C79×#2185 | C2 | semidirect |
| 4. C79×#2001 | C2 | semidirect |
| 5. C79×#1348 | C2 | semidirect |
| 6. C79×#1347 | C2 | semidirect |
| 7. C79×#1314 | C2 | semidirect |
| 180. #12107 | C79 | direct (N × H) |
| 189. #2188 | C2×C79 | semidirect |
| 190. #2185 | C2×C79 | semidirect |
| 191. #2001 | C2×C79 | semidirect |
| 192. #1348 | C2×C79 | semidirect |
| 193. #1347 | C2×C79 | semidirect |
| 194. #1314 | C2×C79 | semidirect |
| 195. C79 | #12107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3191 | 2 |
| C79×#2188 | 2 |
| C79×#2185 | 2 |
| C79×#2001 | 2 |
| C79×#1348 | 2 |
| C79×#1347 | 2 |
| C79×#1314 | 2 |
| #12107 | 79 |