Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1198 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 167 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. #23777171 | C2 | semidirect |
| 2. #23773491 | C2 | semidirect |
| 3. #23762436 | C2 | semidirect |
| 4. #23762334 | C2 | semidirect |
| 5. #23761907 | C2 | semidirect |
| 6. #23761744 | C2 | semidirect |
| 7. C79×#2398 | C2 | semidirect |
| 201. #2398 | D79 | semidirect |
| 206. C79 | #18186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777171 | 2 |
| #23773491 | 2 |
| #23762436 | 2 |
| #23762334 | 2 |
| #23761907 | 2 |
| #23761744 | 2 |
| C79×#2398 | 2 |
| #18186 | 79 |