Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 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. #23774318 | C2 | semidirect |
| 2. #23772866 | C2 | semidirect |
| 3. #23768347 | C2 | semidirect |
| 4. #23761896 | C2 | semidirect |
| 5. #23761792 | C2 | semidirect |
| 6. #23761301 | C2 | semidirect |
| 7. C79×#1545 | C2 | semidirect |
| 40. #14579161 | D4 | semidirect |
| 41. #14579158 | D4 | semidirect |
| 59. C4⋊(C79⋊C8) | D4 | semidirect |
| 77. C4⋊C8×C79 | D4 | semidirect |
| 94. C2×D316 | D8 | semidirect |
| 244. #1545 | D79 | semidirect |
| 248. C79 | #10238 | semidirect |
| 312. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774318 | 2 |
| #23772866 | 2 |
| #23768347 | 2 |
| #23761896 | 2 |
| #23761792 | 2 |
| #23761301 | 2 |
| C79×#1545 | 2 |
| #10238 | 79 |