Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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. C2×#19099004 | C2 | semidirect |
| 3. #23765350 | C2 | semidirect |
| 4. #23765135 | C2 | semidirect |
| 5. #23765021 | C2 | semidirect |
| 6. C79×#3059 | C2 | semidirect |
| 16. #19099004 | C22 | semidirect |
| 19. C2×#14579101 | C22 | semidirect |
| 20. #19098372 | C22 | semidirect |
| 21. #19098345 | C22 | semidirect |
| 22. C22×Q16×C79 | C22 | semidirect |
| 25. #470×C79 | C22 | semidirect |
| 27. #427×C79 | C22 | semidirect |
| 200. #3059 | D79 | semidirect |
| 204. C79 | #33532 | semidirect |
| 213. C22×Q16 | C2×D79 | semidirect |
| 221. #470 | C2×D79 | semidirect |
| 223. #427 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778174 | 2 |
| C2×#19099004 | 2 |
| #23765350 | 2 |
| #23765135 | 2 |
| #23765021 | 2 |
| C79×#3059 | 2 |
| #33532 | 79 |