Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
490 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #23765680 | C2 | semidirect |
| 3. #23765677 | C2 | semidirect |
| 4. #23765675 | C2 | semidirect |
| 7. C79×#2252 | C2 | semidirect |
| 35. C16×D79 | Q8 | semidirect |
| 114. #2252 | D79 | semidirect |
| 117. C79 | #33726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773911 | 2 |
| #23765680 | 2 |
| #23765677 | 2 |
| #23765675 | 2 |
| #23765181 | 2 |
| C4×C16×D79 | 2 |
| C79×#2252 | 2 |
| #33726 | 79 |