Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19098385 | C2 | semidirect |
| 5. #23761511 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 7. C79×#1951 | C2 | semidirect |
| 17. #19098378 | C4 | semidirect |
| 18. #19098375 | C4 | semidirect |
| 149. #1951 | D79 | semidirect |
| 152. C79 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772318 | 2 |
| C2×#19098385 | 2 |
| #23765147 | 2 |
| C2×#19098372 | 2 |
| #23761511 | 2 |
| #23761486 | 2 |
| C79×#1951 | 2 |
| #12952 | 79 |