Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23763117 | C2 | semidirect |
| 3. #23761413 | C2 | semidirect |
| 4. #23761410 | C2 | semidirect |
| 5. C2×C22⋊C16×C79 | C2 | semidirect |
| 6. C2×#14579183 | C4 | semidirect |
| 9. #19098804 | C4 | semidirect |
| 11. #19098799 | C4 | semidirect |
| 15. #19098601 | C4 | semidirect |
| 175. C2×C22⋊C16 | D79 | semidirect |
| 179. C79 | #11703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772981 | 2 |
| #23763117 | 2 |
| #23761413 | 2 |
| #23761410 | 2 |
| C2×C22⋊C16×C79 | 2 |
| #11703 | 79 |