Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
522 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23772483 | C2 | semidirect |
| 3. #23763393 | C2 | semidirect |
| 5. #23761260 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 203. C79 | #9490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772483 | 2 |
| #23768309 | 2 |
| #23763393 | 2 |
| #23761825 | 2 |
| #23761260 | 2 |
| #23761259 | 2 |
| C79×#1486 | 2 |
| #9490 | 79 |