Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 19. #19097705 | C4 | semidirect |
| 20. #19097702 | C4 | semidirect |
| 21. #19097702 | C4 | semidirect |
| 22. #107×C157 | C4 | semidirect |
| 88. C157 | #1922 | semidirect |
| 105. #107 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758280 | 2 |
| #23758238 | 2 |
| #23758149 | 2 |
| #23758143 | 2 |
| (C2×#10597845)⋊C8 | 2 |
| #23757310 | 2 |
| #1922 | 157 |