Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
704 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23771850 | C2 | semidirect |
| 3. #23763338 | C2 | semidirect |
| 4. #23761967 | C2 | semidirect |
| 5. #23761761 | C2 | semidirect |
| 6. #23761287 | C2 | semidirect |
| 7. C79×#1305 | C2 | semidirect |
| 9. C2×#14579189 | C4 | semidirect |
| 10. C2×#14579189 | C4 | semidirect |
| 17. #19098565 | C4 | semidirect |
| 18. #19098565 | C4 | semidirect |
| 286. #1305 | D79 | semidirect |
| 288. C79 | #9347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772654 | 2 |
| #23771850 | 2 |
| #23763338 | 2 |
| #23761967 | 2 |
| #23761761 | 2 |
| #23761287 | 2 |
| C79×#1305 | 2 |
| #9347 | 79 |