Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #23761933 | C2 | semidirect |
| 4. #23761764 | C2 | semidirect |
| 5. #23761309 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 27. #484×C79 | C4 | semidirect |
| 28. #481×C79 | C4 | semidirect |
| 32. #451×C79 | C4 | semidirect |
| 33. #448×C79 | C4 | semidirect |
| 224. C79 | #9331 | semidirect |
| 228. #484 | Dic79 | semidirect |
| 229. #481 | Dic79 | semidirect |
| 233. #451 | Dic79 | semidirect |
| 234. #448 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772462 | 2 |
| #23761956 | 2 |
| #23761933 | 2 |
| #23761764 | 2 |
| #23761309 | 2 |
| #23761276 | 2 |
| C79×#3196 | 2 |
| #9331 | 79 |