Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
706 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23772441 | C2 | semidirect |
| 3. #23762069 | C2 | semidirect |
| 4. #23761301 | C2 | semidirect |
| 5. C79×#1800 | C2 | semidirect |
| 32. C4⋊(C79⋊C8) | D4 | semidirect |
| 155. #1800 | D79 | semidirect |
| 158. C79 | #9405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772441 | 2 |
| #23768346 | 2 |
| #23762069 | 2 |
| #23761301 | 2 |
| C79×#1800 | 2 |
| #9405 | 79 |