Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
962 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 962 conjugacy classes of subgroups — too many to draw. Only its 115 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×#19098361 | C2 | semidirect |
| 3. C2×#19098359 | C2 | semidirect |
| 4. #23763324 | C2 | semidirect |
| 5. C79×#1784 | C2 | semidirect |
| 241. #1784 | D79 | semidirect |
| 242. C79 | #12702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099137 | 2 |
| C2×#19098361 | 2 |
| C2×#19098359 | 2 |
| #23763324 | 2 |
| C79×#1784 | 2 |
| #12702 | 79 |