Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 376 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. #23762170 | C2 | semidirect |
| 5. #23761297 | C2 | semidirect |
| 6. #23761233 | C2 | semidirect |
| 7. C4×C4⋊C8×C79 | C2 | semidirect |
| 15. #19098310 | C4 | semidirect |
| 16. #19098306 | C4 | semidirect |
| 157. C4×C4⋊C8 | D79 | semidirect |
| 163. C79 | #9578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764228 | 2 |
| #23762170 | 2 |
| #23762050 | 2 |
| #23761798 | 2 |
| #23761297 | 2 |
| #23761233 | 2 |
| C4×C4⋊C8×C79 | 2 |
| #9578 | 79 |