Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765583 | C2 | semidirect |
| 2. #23765578 | C2 | semidirect |
| 3. #23764840 | C2 | semidirect |
| 4. #23761415 | C2 | semidirect |
| 5. #23761415 | C2 | semidirect |
| 6. #23761326 | C2 | semidirect |
| 8. C2×#14579095 | C22 | semidirect |
| 14. C22⋊(C79⋊C16) | C22 | semidirect |
| 15. C22⋊(C79⋊C16) | C22 | semidirect |
| 17. #19098328 | C22 | semidirect |
| 171. C79 | #12284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765583 | 2 |
| #23765578 | 2 |
| #23764840 | 2 |
| #23761415 | 2 |
| #23761326 | 2 |
| C79×#3199 | 2 |
| #12284 | 79 |