Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ #408×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#3203 | C2 | semidirect |
| 2. C79×#2187 | C2 | semidirect |
| 3. C79×#2184 | C2 | semidirect |
| 4. C79×#2018 | C2 | semidirect |
| 5. C79×#1350 | C2 | semidirect |
| 6. C79×#1349 | C2 | semidirect |
| 7. C79×#1315 | C2 | semidirect |
| 177. #12110 | C79 | direct (N × H) |
| 185. #3203 | C2×C79 | semidirect |
| 186. #2187 | C2×C79 | semidirect |
| 187. #2184 | C2×C79 | semidirect |
| 188. #2018 | C2×C79 | semidirect |
| 189. #1350 | C2×C79 | semidirect |
| 190. #1349 | C2×C79 | semidirect |
| 191. #1315 | C2×C79 | semidirect |
| 192. C79 | #12110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3203 | 2 |
| C79×#2187 | 2 |
| C79×#2184 | 2 |
| C79×#2018 | 2 |
| C79×#1350 | 2 |
| C79×#1349 | 2 |
| C79×#1315 | 2 |
| #12110 | 79 |