Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
550 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 550 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. #23773404 | C2 | semidirect |
| 3. #23764198 | C2 | semidirect |
| 4. #23761803 | C2 | semidirect |
| 5. #23761799 | C2 | semidirect |
| 6. #23761231 | C2 | semidirect |
| 7. C79×#3135 | C2 | semidirect |
| 206. #3135 | D79 | semidirect |
| 213. C79 | #10033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773404 | 2 |
| #23773396 | 2 |
| #23764198 | 2 |
| #23761803 | 2 |
| #23761799 | 2 |
| #23761231 | 2 |
| C79×#3135 | 2 |
| #10033 | 79 |