Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 1. #23772462 | C2 | semidirect |
| 2. #23761956 | C2 | semidirect |
| 3. #23761929 | C2 | semidirect |
| 4. #23761760 | C2 | semidirect |
| 5. #23761309 | C2 | semidirect |
| 6. #23761276 | C2 | semidirect |
| 26. #483×C79 | C4 | semidirect |
| 28. #480×C79 | C4 | semidirect |
| 31. #450×C79 | C4 | semidirect |
| 33. #447×C79 | C4 | semidirect |
| 233. C79 | #9332 | semidirect |
| 236. #483 | Dic79 | semidirect |
| 238. #480 | Dic79 | semidirect |
| 241. #450 | Dic79 | semidirect |
| 243. #447 | 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 |
| #23761929 | 2 |
| #23761760 | 2 |
| #23761309 | 2 |
| #23761276 | 2 |
| C79×#3194 | 2 |
| #9332 | 79 |