Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#19098358 | C2 | semidirect |
| 2. C2×#19098303 | C2 | semidirect |
| 3. #23761551 | C2 | direct (N × H) |
| 8. #19098358 | C22 | semidirect |
| 10. #19098303 | C22 | semidirect |
| 11. C2×2−1+4×C79 | C4 | semidirect |
| 16. #454×C79 | C4 | semidirect |
| 19. C2×#101×C79 | C4 | semidirect |
| 29. 2−1+4×C79 | C2×C4 | semidirect |
| 52. #101×C79 | C2×C4 | semidirect |
| 176. C2×C79 | #1404 | semidirect |
| 182. C79 | C2×#1404 | semidirect |
| 183. C2×2−1+4 | Dic79 | semidirect |
| 188. #454 | Dic79 | semidirect |
| 191. C2×#101 | Dic79 | semidirect |
| 201. 2−1+4 | C2×Dic79 | semidirect |
| 226. #101 | C2×Dic79 | semidirect |
| 353. C2 | #23761551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098358 | 2 |
| C2×#19098303 | 2 |
| #23761551 | 2 |
| C2×#454×C79 | 2 |
| C2×#1404 | 79 |