Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
496 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #23765120 | C2 | semidirect |
| 5. #23761497 | C2 | semidirect |
| 6. #23761489 | C2 | semidirect |
| 7. C79×#1979 | C2 | semidirect |
| 12. C2×#14579104 | C4 | semidirect |
| 43. C2×C79⋊C16 | C2×C4 | semidirect |
| 53. C2×Q16×C79 | C2×C4 | semidirect |
| 165. #1979 | D79 | semidirect |
| 168. C79 | #13019 | semidirect |
| 194. C2×Q16 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579104 | 2 |
| #23772253 | 2 |
| C2×#19098375 | 2 |
| #23765120 | 2 |
| #23761497 | 2 |
| #23761489 | 2 |
| C79×#1979 | 2 |
| #13019 | 79 |