Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
170 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23765677 | C2 | semidirect |
| 3. #23761601 | C2 | semidirect |
| 4. Dic79⋊C32 | C2 | semidirect |
| 7. C79×#1423 | C2 | semidirect |
| 82. #1423 | D79 | semidirect |
| 86. C79 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765677 | 2 |
| #23765246 | 2 |
| #23761601 | 2 |
| Dic79⋊C32 | 2 |
| #23761579 | 2 |
| #23761577 | 2 |
| C79×#1423 | 2 |
| #13707 | 79 |