Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 82 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 | C24×C79 | D8 |
| 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 |
| 4. C79×#1348 | C2 | semidirect |
| 92. C23×C79 | Q32 | semidirect |
| 140. #12106 | C79 | direct (N × H) |
| 148. #2188 | C2×C79 | semidirect |
| 150. #1348 | C2×C79 | semidirect |
| 152. C79 | #12106 | direct (N × H) |
| 239. C23 | Q32×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3189 | 2 |
| C79×#2188 | 2 |
| C79×#2001 | 2 |
| C79×#1348 | 2 |
| C79×#1314 | 2 |
| #12106 | 79 |