Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765172 | C2 | semidirect |
| 2. #23765165 | C2 | semidirect |
| 6. #23764178 | C2 | semidirect |
| 7. C79×#1386 | C2 | semidirect |
| 146. #1386 | D79 | semidirect |
| 147. C79 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765172 | 2 |
| #23765165 | 2 |
| C2×#19098372 | 2 |
| #23765129 | 2 |
| #23764296 | 2 |
| #23764178 | 2 |
| C79×#1386 | 2 |
| #13469 | 79 |