Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C79 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C79 |
| prime radical | C22×D4×C79 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ C2×C4×D4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C79×#1325 | C2 | semidirect |
| 5. C79×#1324 | C2 | semidirect |
| 166. #11572 | C79 | direct (N × H) |
| 177. #1325 | C2×C79 | semidirect |
| 178. #1324 | C2×C79 | semidirect |
| 179. C79 | #11572 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#2566 | 2 |
| C79×#1465 | 2 |
| C79×#1459 | 2 |
| C79×#1325 | 2 |
| C79×#1324 | 2 |
| #11572 | 79 |