Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1258 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 191 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. #23774327 | C2 | semidirect |
| 3. #23768573 | C2 | semidirect |
| 4. #23762354 | C2 | semidirect |
| 5. #23761896 | C2 | semidirect |
| 6. C79×#1460 | C2 | semidirect |
| 14. C2×#14579161 | C22 | semidirect |
| 19. #19098704 | C22 | semidirect |
| 20. #19098475 | C22 | semidirect |
| 24. C4×C4⋊Dic79 | C22 | semidirect |
| 25. #19098298 | C22 | semidirect |
| 27. #431×C79 | C22 | semidirect |
| 28. #323×C79 | C22 | semidirect |
| 111. C2×D4×C79 | SD16 | semidirect |
| 200. #1460 | D79 | semidirect |
| 201. C79 | #18388 | semidirect |
| 216. #431 | C2×D79 | semidirect |
| 223. #323 | C2×D79 | semidirect |
| 289. C2×D4 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777164 | 2 |
| #23774327 | 2 |
| #23768573 | 2 |
| #23762354 | 2 |
| #23761896 | 2 |
| C79×#1460 | 2 |
| #18388 | 79 |