Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #23761258 | C2 | semidirect |
| 4. #23761233 | C2 | semidirect |
| 5. C79×#2862 | C2 | semidirect |
| 19. #14579161 | Q8 | semidirect |
| 20. #14579158 | Q8 | semidirect |
| 127. #2862 | D79 | semidirect |
| 132. C79 | #10362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764228 | 2 |
| #23761959 | 2 |
| #23761258 | 2 |
| #23761233 | 2 |
| C79×#2862 | 2 |
| #10362 | 79 |