Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
442 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23765147 | C2 | semidirect |
| 3. #23765135 | C2 | semidirect |
| 4. #23761480 | C2 | semidirect |
| 5. C79×#1946 | C2 | semidirect |
| 48. #106×C79 | D4 | semidirect |
| 136. #1946 | D79 | semidirect |
| 138. C79 | #13416 | semidirect |
| 181. #106 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773846 | 2 |
| #23765147 | 2 |
| #23765135 | 2 |
| #23761480 | 2 |
| C79×#1946 | 2 |
| #13416 | 79 |