Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
612 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23761972 | C2 | semidirect |
| 5. #23761268 | C2 | semidirect |
| 6. #23761267 | C2 | semidirect |
| 7. C79×#1520 | C2 | semidirect |
| 10. #19098498 | C4 | semidirect |
| 12. #19098474 | C4 | semidirect |
| 232. #1520 | D79 | semidirect |
| 236. C79 | #9201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769207 | 2 |
| #23765997 | 2 |
| #23761972 | 2 |
| C2×#19098286 | 2 |
| #23761268 | 2 |
| #23761267 | 2 |
| C79×#1520 | 2 |
| #9201 | 79 |