Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #23762174 | C2 | semidirect |
| 4. #23762084 | C2 | semidirect |
| 5. #23762082 | C2 | semidirect |
| 7. C79×#1301 | C2 | semidirect |
| 168. #1301 | D79 | semidirect |
| 169. C79 | #10453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098854 | 2 |
| #23763389 | 2 |
| #23762174 | 2 |
| #23762084 | 2 |
| #23762082 | 2 |
| #23761792 | 2 |
| C79×#1301 | 2 |
| #10453 | 79 |