Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
290 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×#19097840 | C2 | semidirect |
| 4. C4⋊C4×#10597845 | C2 | semidirect |
| 5. #23758146 | C2 | semidirect |
| 6. (C2×#10597845)⋊C8 | C2 | semidirect |
| 21. #19097693 | C4 | semidirect |
| 22. #19097692 | C4 | semidirect |
| 23. #19097691 | C4 | semidirect |
| 24. #102×C157 | C4 | semidirect |
| 134. C157 | #1925 | semidirect |
| 158. #102 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097840 | 2 |
| C2×#19097833 | 2 |
| #23758225 | 2 |
| C4⋊C4×#10597845 | 2 |
| #23758146 | 2 |
| (C2×#10597845)⋊C8 | 2 |
| #102×D157 | 2 |
| #1925 | 157 |