Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23761435 | C2 | semidirect |
| 5. #23761434 | C2 | semidirect |
| 6. #23761434 | C2 | semidirect |
| 7. C79×#1356 | C2 | semidirect |
| 137. #1356 | D79 | semidirect |
| 138. C79 | #11914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774058 | 2 |
| #23765214 | 2 |
| #23765003 | 2 |
| #23761435 | 2 |
| #23761434 | 2 |
| C79×#1356 | 2 |
| #11914 | 79 |