Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
880 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 880 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 |
|---|---|---|
| 1. #23772429 | C2 | semidirect |
| 2. #23763321 | C2 | semidirect |
| 3. #23761738 | C2 | semidirect |
| 4. #23761306 | C2 | semidirect |
| 24. C2×#11929608 | D4 | semidirect |
| 129. C23×C79 | #100 | semidirect |
| 203. C79 | #9503 | semidirect |
| 327. C23 | #14579078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772429 | 2 |
| #23763321 | 2 |
| #23761738 | 2 |
| #23761306 | 2 |
| C79×#2408 | 2 |
| #9503 | 79 |