Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
574 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #23774523 | C2 | semidirect |
| 2. #23774518 | C2 | semidirect |
| 4. #23764219 | C2 | semidirect |
| 5. #23761959 | C2 | semidirect |
| 6. #23761244 | C2 | semidirect |
| 7. C79×#1517 | C2 | semidirect |
| 203. #1517 | D79 | semidirect |
| 205. C79 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774523 | 2 |
| #23774518 | 2 |
| #23773845 | 2 |
| #23764219 | 2 |
| #23761959 | 2 |
| #23761244 | 2 |
| C79×#1517 | 2 |
| #10225 | 79 |