Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23774383 | C2 | semidirect |
| 2. #23773868 | C2 | semidirect |
| 3. #23761869 | C2 | semidirect |
| 4. #23761817 | C2 | semidirect |
| 5. #23761753 | C2 | semidirect |
| 6. #23761273 | C2 | semidirect |
| 7. C79×#3214 | C2 | semidirect |
| 213. #3214 | D79 | semidirect |
| 220. C79 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774383 | 2 |
| #23773868 | 2 |
| #23761869 | 2 |
| #23761817 | 2 |
| #23761753 | 2 |
| #23761273 | 2 |
| C79×#3214 | 2 |
| #10120 | 79 |