Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23763392 | C2 | semidirect |
| 3. #23761407 | C2 | semidirect |
| 4. #23761404 | C2 | semidirect |
| 5. C79×#1459 | C2 | semidirect |
| 206. #1459 | D79 | semidirect |
| 209. C79 | #11884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768356 | 2 |
| #23763392 | 2 |
| #23761407 | 2 |
| #23761404 | 2 |
| C79×#1459 | 2 |
| #11884 | 79 |