Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
934 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 183 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. #23762442 | C2 | semidirect |
| 5. #23761912 | C2 | semidirect |
| 6. #23761744 | C2 | semidirect |
| 7. C79×#3502 | C2 | semidirect |
| 183. #3502 | D79 | semidirect |
| 190. C79 | #18188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773495 | 2 |
| #23766683 | 2 |
| #23762442 | 2 |
| #23762340 | 2 |
| #23761912 | 2 |
| #23761744 | 2 |
| C79×#3502 | 2 |
| #18188 | 79 |