Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C79 | #99 |
| commutator | C22×C4 | C22×C4×C79 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C79 |
| socle | C22×C79 | C2×#99 |
| prime radical | C22×D4×C79 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×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×#1351 | C2 | semidirect |
| 5. C79×#1344 | C2 | semidirect |
| 6. C2×C4×Q8×C79 | C4 | semidirect |
| 11. #397×C79 | C4 | semidirect |
| 14. #393×C79 | C4 | semidirect |
| 19. #376×C79 | C4 | semidirect |
| 171. #11728 | C79 | direct (N × H) |
| 182. #1351 | C2×C79 | semidirect |
| 183. #1344 | C2×C79 | semidirect |
| 184. C79 | #11728 | direct (N × H) |
| 185. C2×C4×Q8 | C4×C79 | semidirect |
| 190. #397 | C4×C79 | semidirect |
| 193. #393 | C4×C79 | semidirect |
| 198. #376 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#2398 | 2 |
| C4×#99×C79 | 2 |
| C79×#1459 | 2 |
| C79×#1351 | 2 |
| C79×#1344 | 2 |
| #11728 | 79 |