Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23773440 | C2 | semidirect |
| 4. #23764340 | C2 | semidirect |
| 5. #23761804 | C2 | semidirect |
| 7. C79×#1275 | C2 | semidirect |
| 199. #1275 | D79 | semidirect |
| 200. C79 | #10035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773746 | 2 |
| #23773440 | 2 |
| #23773432 | 2 |
| #23764340 | 2 |
| #23761804 | 2 |
| #23761800 | 2 |
| C79×#1275 | 2 |
| #10035 | 79 |