Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
946 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23774778 | C2 | semidirect |
| 2. #23773725 | C2 | semidirect |
| 3. #23762551 | C2 | semidirect |
| 4. #23762489 | C2 | semidirect |
| 5. #23762138 | C2 | semidirect |
| 6. #23761851 | C2 | semidirect |
| 7. C79×#3548 | C2 | semidirect |
| 170. #3548 | D79 | semidirect |
| 177. C79 | #18696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774778 | 2 |
| #23773725 | 2 |
| #23762551 | 2 |
| #23762489 | 2 |
| #23762138 | 2 |
| #23761851 | 2 |
| C79×#3548 | 2 |
| #18696 | 79 |