Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
816 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23764370 | C2 | semidirect |
| 3. #23764216 | C2 | semidirect |
| 4. C2×#19098302 | C2 | semidirect |
| 5. C2×#330×C79 | C2 | semidirect |
| 8. #19099311 | C4 | semidirect |
| 158. C2×#330 | D79 | semidirect |
| 160. C79 | #8508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099311 | 2 |
| #23764370 | 2 |
| #23764216 | 2 |
| C2×#19098302 | 2 |
| C2×#330×C79 | 2 |
| #8508 | 79 |