Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 172 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. #23765676 | C2 | semidirect |
| 5. #23761475 | C2 | semidirect |
| 6. #23761462 | C2 | semidirect |
| 7. C79×#1366 | C2 | semidirect |
| 92. #1366 | D79 | semidirect |
| 93. C79 | #12464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765676 | 2 |
| #23765577 | 2 |
| #23765573 | 2 |
| #23765236 | 2 |
| #23761475 | 2 |
| #23761462 | 2 |
| C79×#1366 | 2 |
| #12464 | 79 |