Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23761462 | C2 | semidirect |
| 5. #23761460 | C2 | semidirect |
| 6. #23761439 | C2 | semidirect |
| 7. C79×#1358 | C2 | semidirect |
| 116. #1358 | D79 | semidirect |
| 117. C79 | #11990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774056 | 2 |
| #23765215 | 2 |
| #23765164 | 2 |
| #23761462 | 2 |
| #23761460 | 2 |
| #23761439 | 2 |
| C79×#1358 | 2 |
| #11990 | 79 |