Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. #23776534 | C2 | semidirect |
| 2. #23765128 | C2 | semidirect |
| 3. #23764293 | C2 | semidirect |
| 4. #23761480 | C2 | semidirect |
| 5. C79×#3150 | C2 | semidirect |
| 26. C2×Dic316 | D4 | semidirect |
| 28. C2×D632 | D4 | semidirect |
| 36. C2×C79⋊C16 | D4 | semidirect |
| 165. #3150 | D79 | semidirect |
| 169. C79 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23765128 | 2 |
| #23764293 | 2 |
| #23761480 | 2 |
| C79×#3150 | 2 |
| #13340 | 79 |