Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23765201 | C2 | semidirect |
| 3. #23762154 | C2 | semidirect |
| 4. #23761368 | C2 | semidirect |
| 5. #23761367 | C2 | semidirect |
| 6. #23761366 | C2 | semidirect |
| 7. C79×#1333 | C2 | semidirect |
| 21. #19098339 | C22 | semidirect |
| 22. #19098314 | C22 | semidirect |
| 25. #346×C79 | C22 | semidirect |
| 26. #334×C79 | C22 | semidirect |
| 76. D632 | M16 | semidirect |
| 97. D8×C79 | M16 | semidirect |
| 173. #1333 | D79 | semidirect |
| 174. C79 | #11663 | semidirect |
| 190. #346 | C2×D79 | semidirect |
| 193. #334 | C2×D79 | semidirect |
| 248. D8 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D79 | 2 |
| #23765201 | 2 |
| #23762154 | 2 |
| #23761368 | 2 |
| #23761367 | 2 |
| #23761366 | 2 |
| C79×#1333 | 2 |
| #11663 | 79 |