Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 1. C2×#19098392 | C2 | semidirect |
| 4. #23763282 | C2 | semidirect |
| 5. #23761496 | C2 | semidirect |
| 6. #23761477 | C2 | semidirect |
| 16. #19098367 | C4 | semidirect |
| 17. #19098367 | C4 | semidirect |
| 18. #19098364 | C4 | semidirect |
| 19. #19098364 | C4 | semidirect |
| 161. C79 | #13134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098392 | 2 |
| #23765107 | 2 |
| #23764289 | 2 |
| #23763282 | 2 |
| #23761496 | 2 |
| #23761477 | 2 |
| C2×#359×C79 | 2 |
| #13134 | 79 |