Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #23761792 | C2 | semidirect |
| 3. #23761720 | C2 | semidirect |
| 4. #23761692 | C2 | semidirect |
| 5. C79×#1564 | C2 | semidirect |
| 143. #1564 | D79 | semidirect |
| 147. C79 | #9670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D632 | 2 |
| #23761792 | 2 |
| #23761720 | 2 |
| #23761692 | 2 |
| C79×#1564 | 2 |
| #9670 | 79 |