Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23773400 | C2 | semidirect |
| 2. #23772866 | C2 | semidirect |
| 3. #23768301 | C2 | semidirect |
| 4. #23761961 | C2 | semidirect |
| 5. #23761790 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#1486 | C2 | semidirect |
| 42. #14579161 | D4 | semidirect |
| 43. #14579158 | D4 | semidirect |
| 67. C4×C79⋊C8 | D4 | semidirect |
| 83. C4⋊C8×C79 | D4 | semidirect |
| 100. C2×D316 | D8 | semidirect |
| 261. #1486 | D79 | semidirect |
| 264. C79 | #9996 | semidirect |
| 331. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773400 | 2 |
| #23772866 | 2 |
| #23768301 | 2 |
| #23761961 | 2 |
| #23761790 | 2 |
| #23761260 | 2 |
| C79×#1486 | 2 |
| #9996 | 79 |