Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23761742 | C2 | semidirect |
| 3. #23761722 | C2 | semidirect |
| 4. #23761332 | C2 | semidirect |
| 5. #23761331 | C2 | semidirect |
| 6. #23761331 | C2 | semidirect |
| 7. C79×#1318 | C2 | semidirect |
| 215. #1318 | D79 | semidirect |
| 216. C79 | #11567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768404 | 2 |
| #23761742 | 2 |
| #23761722 | 2 |
| #23761332 | 2 |
| #23761331 | 2 |
| C79×#1318 | 2 |
| #11567 | 79 |