Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 2. C2×C22⋊(C79⋊C16) | C2 | semidirect |
| 3. #23761417 | C2 | semidirect |
| 4. #23761414 | C2 | semidirect |
| 5. C79×#1810 | C2 | semidirect |
| 170. #1810 | D79 | semidirect |
| 173. C79 | #11893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772981 | 2 |
| C2×C22⋊(C79⋊C16) | 2 |
| #23761417 | 2 |
| #23761414 | 2 |
| C79×#1810 | 2 |
| #11893 | 79 |