Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
582 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23763571 | C2 | semidirect |
| 3. #23762069 | C2 | semidirect |
| 4. #23762068 | C2 | semidirect |
| 5. #23762067 | C2 | semidirect |
| 6. #23761684 | C2 | semidirect |
| 7. C79×#1545 | C2 | semidirect |
| 173. #1545 | D79 | semidirect |
| 175. C79 | #9773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098939 | 2 |
| #23763571 | 2 |
| #23762069 | 2 |
| #23762068 | 2 |
| #23762067 | 2 |
| #23761684 | 2 |
| C79×#1545 | 2 |
| #9773 | 79 |