Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765679 | C2 | semidirect |
| 2. #23761601 | C2 | semidirect |
| 3. #23761599 | C2 | semidirect |
| 4. C4⋊(C79⋊C32) | C2 | semidirect |
| 86. C79 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765679 | 2 |
| #23761601 | 2 |
| #23761599 | 2 |
| C4⋊(C79⋊C32) | 2 |
| #23761578 | 2 |
| C4×D16×C79 | 2 |
| #13707 | 79 |