Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
908 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 169 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. #23772303 | C2 | semidirect |
| 2. #23772106 | C2 | semidirect |
| 3. #23764953 | C2 | semidirect |
| 4. #23764917 | C2 | semidirect |
| 5. #23764464 | C2 | semidirect |
| 6. #23763156 | C2 | semidirect |
| 7. C79×#2017 | C2 | semidirect |
| 43. #14579071 | D4 | semidirect |
| 44. C8×Dic79 | D4 | semidirect |
| 128. #2017 | D79 | semidirect |
| 131. C79 | #23795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772303 | 2 |
| #23772106 | 2 |
| #23764953 | 2 |
| #23764917 | 2 |
| #23764464 | 2 |
| #23763156 | 2 |
| C79×#2017 | 2 |
| #23795 | 79 |