Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23766483 | C2 | semidirect |
| 4. #23761973 | C2 | semidirect |
| 6. #23761280 | C2 | semidirect |
| 7. C79×#1282 | C2 | semidirect |
| 10. #19098894 | C4 | semidirect |
| 13. #19098716 | C4 | semidirect |
| 137. C22⋊C4×C79 | SD16 | semidirect |
| 250. #1282 | D79 | semidirect |
| 251. C79 | #9278 | semidirect |
| 379. C22⋊C4 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774158 | 2 |
| #23766483 | 2 |
| #23764236 | 2 |
| #23761973 | 2 |
| C2×#19098298 | 2 |
| #23761280 | 2 |
| C79×#1282 | 2 |
| #9278 | 79 |