Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
630 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #23765074 | C2 | semidirect |
| 4. #23765055 | C2 | semidirect |
| 5. #23761530 | C2 | semidirect |
| 6. #23761520 | C2 | semidirect |
| 8. C2×#14579191 | C4 | semidirect |
| 9. C22×#11929614 | C4 | semidirect |
| 16. #19098572 | C4 | semidirect |
| 17. #19098559 | C4 | semidirect |
| 248. C79 | #13101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772695 | 2 |
| #23771864 | 2 |
| #23765074 | 2 |
| #23765055 | 2 |
| #23761530 | 2 |
| #23761520 | 2 |
| C79×#1796 | 2 |
| #13101 | 79 |