Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19098383 | C2 | semidirect |
| 5. #23764149 | C2 | semidirect |
| 6. #23761508 | C2 | semidirect |
| 7. C79×#2159 | C2 | semidirect |
| 147. #2159 | D79 | semidirect |
| 154. C79 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098383 | 2 |
| C2×#19098377 | 2 |
| #23765115 | 2 |
| #23764264 | 2 |
| #23764149 | 2 |
| #23761508 | 2 |
| C79×#2159 | 2 |
| #13478 | 79 |