Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #23761575 | C2 | semidirect |
| 11. #533×C79 | C4 | semidirect |
| 13. #488×C79 | C4 | semidirect |
| 19. C2×C4×C8×C79 | C4 | semidirect |
| 137. C79 | #13602 | semidirect |
| 138. #533 | Dic79 | semidirect |
| 140. #488 | Dic79 | semidirect |
| 148. C2×C4×C8 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765085 | 2 |
| #23765065 | 2 |
| #23761575 | 2 |
| C79×#3131 | 2 |
| #13602 | 79 |