Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23772487 | C2 | semidirect |
| 4. #23761848 | C2 | semidirect |
| 6. #23761270 | C2 | semidirect |
| 7. C79×#1283 | C2 | semidirect |
| 216. #1283 | D79 | semidirect |
| 217. C79 | #9244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098786 | 2 |
| #23772487 | 2 |
| #23761997 | 2 |
| #23761848 | 2 |
| #23761751 | 2 |
| #23761270 | 2 |
| C79×#1283 | 2 |
| #9244 | 79 |