Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
622 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. #23766018 | C2 | semidirect |
| 3. C2×#19098289 | C2 | semidirect |
| 4. #23761267 | C2 | semidirect |
| 16. #398×C79 | C4 | semidirect |
| 18. #394×C79 | C4 | semidirect |
| 193. C79 | #9204 | semidirect |
| 199. #398 | Dic79 | semidirect |
| 201. #394 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766018 | 2 |
| #23761968 | 2 |
| C2×#19098289 | 2 |
| #23761267 | 2 |
| C79×#2618 | 2 |
| #9204 | 79 |