Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23765120 | C2 | semidirect |
| 4. #23761507 | C2 | semidirect |
| 17. #470×C79 | C4 | semidirect |
| 39. C2×Q16×C79 | C2×C4 | semidirect |
| 52. #106×C79 | C2×C4 | semidirect |
| 153. C79 | #13000 | semidirect |
| 160. #470 | Dic79 | semidirect |
| 173. C2×Q16 | C2×Dic79 | semidirect |
| 200. #106 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771990 | 2 |
| #23765120 | 2 |
| C2×#19098345 | 2 |
| #23761507 | 2 |
| C2×#470×C79 | 2 |
| #13000 | 79 |