Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23771964 | C2 | semidirect |
| 3. #23762067 | C2 | semidirect |
| 4. #23761259 | C2 | semidirect |
| 5. C79×#1458 | C2 | semidirect |
| 42. C4⋊(C79⋊C8) | D4 | semidirect |
| 188. #1458 | D79 | semidirect |
| 190. C79 | #9197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771964 | 2 |
| #23769150 | 2 |
| #23762067 | 2 |
| #23761259 | 2 |
| C79×#1458 | 2 |
| #9197 | 79 |