Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 4. #23761248 | C2 | semidirect |
| 5. #23761247 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 7. C79×#1282 | C2 | semidirect |
| 247. #1282 | D79 | semidirect |
| 248. C79 | #8736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765995 | 2 |
| C2×#19098286 | 2 |
| #23761248 | 2 |
| #23761247 | 2 |
| #23761246 | 2 |
| C79×#1282 | 2 |
| #8736 | 79 |