Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #23761951 | C2 | semidirect |
| 5. #23761847 | C2 | semidirect |
| 6. #23761266 | C2 | semidirect |
| 7. C79×#3113 | C2 | semidirect |
| 197. #3113 | D79 | semidirect |
| 203. C79 | #10024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773789 | 2 |
| #23769260 | 2 |
| #23762023 | 2 |
| #23761951 | 2 |
| #23761847 | 2 |
| #23761266 | 2 |
| C79×#3113 | 2 |
| #10024 | 79 |