Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23765674 | C2 | semidirect |
| 3. #23761601 | C2 | semidirect |
| 4. Dic79⋊C32 | C2 | semidirect |
| 7. C79×#1424 | C2 | semidirect |
| 23. D1264 | Q8 | semidirect |
| 83. #1424 | D79 | semidirect |
| 87. C79 | #13705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765674 | 2 |
| #23765246 | 2 |
| #23761601 | 2 |
| Dic79⋊C32 | 2 |
| #23761579 | 2 |
| #23761577 | 2 |
| C79×#1424 | 2 |
| #13705 | 79 |