Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23772117 | C2 | semidirect |
| 3. #23764197 | C2 | semidirect |
| 4. #23762050 | C2 | semidirect |
| 5. #23761824 | C2 | semidirect |
| 6. #23761244 | C2 | semidirect |
| 7. C79×#1301 | C2 | semidirect |
| 102. C2×C79⋊C8 | D8 | semidirect |
| 213. #1301 | D79 | semidirect |
| 215. C79 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773401 | 2 |
| #23772117 | 2 |
| #23764197 | 2 |
| #23762050 | 2 |
| #23761824 | 2 |
| #23761244 | 2 |
| C79×#1301 | 2 |
| #9049 | 79 |