Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
734 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23773401 | C2 | semidirect |
| 2. #23773400 | C2 | semidirect |
| 3. #23766679 | C2 | semidirect |
| 4. #23764231 | C2 | semidirect |
| 5. #23761824 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#1486 | C2 | semidirect |
| 39. #14579161 | D4 | semidirect |
| 40. #14579158 | D4 | semidirect |
| 67. C4×C79⋊C8 | D4 | semidirect |
| 84. C4×C8×C79 | D4 | semidirect |
| 121. C4×Dic79 | D8 | semidirect |
| 241. #1486 | D79 | semidirect |
| 243. C79 | #10012 | semidirect |
| 318. C4×C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773401 | 2 |
| #23773400 | 2 |
| #23766679 | 2 |
| #23764231 | 2 |
| #23761824 | 2 |
| #23761228 | 2 |
| C79×#1486 | 2 |
| #10012 | 79 |