Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 1. #23776534 | C2 | semidirect |
| 2. #23773120 | C2 | semidirect |
| 3. C2×#19098370 | C2 | semidirect |
| 4. C2×#19098369 | C2 | semidirect |
| 5. #23765014 | C2 | semidirect |
| 6. #23761503 | C2 | semidirect |
| 7. C79×#3067 | C2 | semidirect |
| 225. #3067 | D79 | semidirect |
| 230. C79 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23773120 | 2 |
| C2×#19098370 | 2 |
| C2×#19098369 | 2 |
| #23765014 | 2 |
| #23761503 | 2 |
| C79×#3067 | 2 |
| #13312 | 79 |