Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23766206 | C2 | semidirect |
| 3. #23762002 | C2 | semidirect |
| 5. #23761266 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 25. #501×C79 | C4 | semidirect |
| 26. #490×C79 | C4 | semidirect |
| 205. C79 | #9382 | semidirect |
| 208. #501 | Dic79 | semidirect |
| 209. #490 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766206 | 2 |
| #23764320 | 2 |
| #23762002 | 2 |
| #23761947 | 2 |
| #23761266 | 2 |
| #23761255 | 2 |
| C79×#3234 | 2 |
| #9382 | 79 |