Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
734 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 734 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. #23773396 | C2 | semidirect |
| 2. #23766679 | C2 | semidirect |
| 3. #23764233 | C2 | semidirect |
| 4. #23761826 | C2 | semidirect |
| 5. #23761825 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 7. C79×#3100 | C2 | semidirect |
| 58. C4×C79⋊C8 | D4 | semidirect |
| 65. C4⋊Q8×C79 | D4 | semidirect |
| 66. #127×C79 | D4 | semidirect |
| 84. C4×C8×C79 | D4 | semidirect |
| 110. C4×Dic79 | D8 | semidirect |
| 237. #3100 | D79 | semidirect |
| 243. C79 | #10012 | semidirect |
| 278. C4⋊Q8 | C22⋊D79 | semidirect |
| 279. #127 | C22⋊D79 | 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 |
|---|---|
| #23773396 | 2 |
| #23766679 | 2 |
| #23764233 | 2 |
| #23761826 | 2 |
| #23761825 | 2 |
| #23761228 | 2 |
| C79×#3100 | 2 |
| #10012 | 79 |