Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23765174 | C2 | semidirect |
| 2. #23765166 | C2 | semidirect |
| 6. #23761507 | C2 | semidirect |
| 7. C79×#1951 | C2 | semidirect |
| 145. #1951 | D79 | semidirect |
| 147. C79 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765174 | 2 |
| #23765166 | 2 |
| C2×#19098372 | 2 |
| #23765127 | 2 |
| #23764298 | 2 |
| #23761507 | 2 |
| C79×#1951 | 2 |
| #13469 | 79 |