Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19098933 | C2 | semidirect |
| 3. C2×#19098923 | C2 | semidirect |
| 4. #23762724 | C2 | direct (N × H) |
| 5. C2×#19098302 | C2 | semidirect |
| 6. C2×#330×C79 | C2 | semidirect |
| 16. #19098933 | C22 | semidirect |
| 18. #19098923 | C22 | semidirect |
| 23. #19098302 | C22 | semidirect |
| 26. #330×C79 | C22 | semidirect |
| 145. C2×C79 | #1662 | semidirect |
| 153. C2×#330 | D79 | semidirect |
| 155. C79 | C2×#1662 | semidirect |
| 174. #330 | C2×D79 | semidirect |
| 294. C2 | #23762724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099311 | 2 |
| C2×#19098933 | 2 |
| C2×#19098923 | 2 |
| #23762724 | 2 |
| C2×#19098302 | 2 |
| C2×#330×C79 | 2 |
| C2×#1662 | 79 |