Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23775010 | C2 | semidirect |
| 2. #23765664 | C2 | semidirect |
| 3. #23762876 | C2 | semidirect |
| 4. #23761444 | C2 | semidirect |
| 5. #23761367 | C2 | semidirect |
| 6. #23761357 | C2 | semidirect |
| 7. C79×#2206 | C2 | semidirect |
| 19. #19098339 | C22 | semidirect |
| 20. #19098314 | C22 | semidirect |
| 23. #493×C79 | C22 | semidirect |
| 25. C4⋊C16×C79 | C22 | semidirect |
| 107. D8×C79 | D8 | semidirect |
| 182. #2206 | D79 | semidirect |
| 187. C79 | #12324 | semidirect |
| 194. #493 | C2×D79 | semidirect |
| 202. C4⋊C16 | C2×D79 | semidirect |
| 275. D8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775010 | 2 |
| #23765664 | 2 |
| #23762876 | 2 |
| #23761444 | 2 |
| #23761367 | 2 |
| #23761357 | 2 |
| C79×#2206 | 2 |
| #12324 | 79 |