Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. #23771990 | C2 | semidirect |
| 2. #23765116 | C2 | semidirect |
| 3. C2×#19098345 | C2 | semidirect |
| 4. #23761507 | C2 | semidirect |
| 17. #469×C79 | C4 | semidirect |
| 31. #14579095 | D4 | semidirect |
| 40. C2×D8×C79 | C2×C4 | semidirect |
| 52. #106×C79 | C2×C4 | semidirect |
| 162. C79 | #12999 | semidirect |
| 169. #469 | Dic79 | semidirect |
| 183. C2×D8 | C2×Dic79 | semidirect |
| 209. #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 |
| #23765116 | 2 |
| C2×#19098345 | 2 |
| #23761507 | 2 |
| C2×#469×C79 | 2 |
| #12999 | 79 |