Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
274 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23765441 | C2 | semidirect |
| 2. #23765437 | C2 | semidirect |
| 4. #23762206 | C2 | semidirect |
| 5. #23761469 | C2 | semidirect |
| 6. #23761445 | C2 | semidirect |
| 7. C79×#1361 | C2 | semidirect |
| 51. Dic316 | D8 | semidirect |
| 101. C79⋊C8 | SD32 | semidirect |
| 128. #1361 | D79 | semidirect |
| 129. C79 | #12425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765441 | 2 |
| #23765437 | 2 |
| #23763014 | 2 |
| #23762206 | 2 |
| #23761469 | 2 |
| #23761445 | 2 |
| C79×#1361 | 2 |
| #12425 | 79 |