Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
574 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23765765 | C2 | semidirect |
| 5. #23761294 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#1491 | C2 | semidirect |
| 11. #19098858 | C4 | semidirect |
| 12. #19098763 | C4 | semidirect |
| 121. Q8×C79 | #104 | semidirect |
| 188. #1491 | D79 | semidirect |
| 191. C79 | #9326 | semidirect |
| 306. Q8 | #14579087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773522 | 2 |
| #23765765 | 2 |
| #23764319 | 2 |
| #23761909 | 2 |
| #23761294 | 2 |
| #23761255 | 2 |
| C79×#1491 | 2 |
| #9326 | 79 |