Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
472 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19098380 | C2 | semidirect |
| 5. #23764271 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#1375 | C2 | semidirect |
| 13. C2×Dic632 | C4 | semidirect |
| 14. C2×#14579106 | C4 | semidirect |
| 176. #1375 | D79 | semidirect |
| 177. C79 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099006 | 2 |
| C2×#19098686 | 2 |
| C2×#19098380 | 2 |
| C2×#19098374 | 2 |
| #23764271 | 2 |
| #23761499 | 2 |
| C79×#1375 | 2 |
| #13039 | 79 |