Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
438 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23772470 | C2 | semidirect |
| 3. #23762103 | C2 | semidirect |
| 4. #23762023 | C2 | semidirect |
| 5. #23761751 | C2 | semidirect |
| 6. C79⋊#1308 | C2 | semidirect |
| 7. C79×#1287 | C2 | semidirect |
| 172. #1287 | D79 | semidirect |
| 173. C79 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774389 | 2 |
| #23772470 | 2 |
| #23762103 | 2 |
| #23762023 | 2 |
| #23761751 | 2 |
| C79⋊#1308 | 2 |
| C79×#1287 | 2 |
| #9333 | 79 |