Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 15. #19098312 | C4 | semidirect |
| 16. #19098309 | C4 | semidirect |
| 146. C79 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C79⋊C8) | 2 |
| #23762172 | 2 |
| #23762057 | 2 |
| #23761803 | 2 |
| #23761295 | 2 |
| #23761233 | 2 |
| C79×#1994 | 2 |
| #9579 | 79 |