Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
680 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #23766572 | C2 | semidirect |
| 3. C2×#19098359 | C2 | semidirect |
| 4. #23763359 | C2 | semidirect |
| 5. #23761527 | C2 | semidirect |
| 6. #23761526 | C2 | semidirect |
| 7. C79×#1793 | C2 | semidirect |
| 11. #19098736 | C4 | semidirect |
| 59. #14579080 | C2×C4 | semidirect |
| 68. 2−1+4×C79 | C2×C4 | semidirect |
| 269. #1793 | D79 | semidirect |
| 272. C79 | #13055 | semidirect |
| 299. 2−1+4 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098736 | 2 |
| #23766572 | 2 |
| C2×#19098359 | 2 |
| #23763359 | 2 |
| #23761527 | 2 |
| #23761526 | 2 |
| C79×#1793 | 2 |
| #13055 | 79 |