Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23772060 | C2 | semidirect |
| 3. #23763497 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 7. C79×#1293 | C2 | semidirect |
| 17. C2×#14579095 | C4 | semidirect |
| 18. C2×#14579093 | C4 | semidirect |
| 20. C2×#14579083 | C4 | semidirect |
| 21. C2×#14579083 | C4 | semidirect |
| 229. #1293 | D79 | semidirect |
| 231. C79 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098888 | 2 |
| #23772060 | 2 |
| #23763497 | 2 |
| #23761917 | 2 |
| #23761761 | 2 |
| #23761247 | 2 |
| C79×#1293 | 2 |
| #9242 | 79 |