Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 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. #23765021 | C2 | semidirect |
| 2. #23763446 | C2 | semidirect |
| 3. #23761388 | C2 | semidirect |
| 4. #23761385 | C2 | semidirect |
| 12. C2×#135×C79 | C4 | semidirect |
| 15. #470×C79 | C4 | semidirect |
| 17. #469×C79 | C4 | semidirect |
| 21. C2×#106×C79 | C4 | semidirect |
| 177. C79 | #11867 | semidirect |
| 178. C2×#135 | Dic79 | semidirect |
| 182. #470 | Dic79 | semidirect |
| 184. #469 | Dic79 | semidirect |
| 189. C2×#106 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765021 | 2 |
| #23763446 | 2 |
| #23761388 | 2 |
| #23761385 | 2 |
| C79×#3060 | 2 |
| #11867 | 79 |