Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
572 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 151 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. #23773979 | C2 | semidirect |
| 2. #23765548 | C2 | semidirect |
| 3. #23765503 | C2 | semidirect |
| 4. #23765436 | C2 | semidirect |
| 5. C79×#2150 | C2 | semidirect |
| 110. #2150 | D79 | semidirect |
| 111. C79 | #33819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773979 | 2 |
| #23765548 | 2 |
| #23765503 | 2 |
| #23765436 | 2 |
| C79×#2150 | 2 |
| #33819 | 79 |