Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 1. C2×#19097842 | C2 | semidirect |
| 4. #23758238 | C2 | semidirect |
| 5. #23758143 | C2 | semidirect |
| 6. (C2×#10597845)⋊C8 | C2 | semidirect |
| 21. #19097696 | C4 | semidirect |
| 22. #19097694 | C4 | semidirect |
| 23. #19097692 | C4 | semidirect |
| 24. #102×C157 | C4 | semidirect |
| 105. C157 | #1929 | semidirect |
| 126. #102 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097842 | 2 |
| C2×#19097835 | 2 |
| #23758247 | 2 |
| #23758238 | 2 |
| #23758143 | 2 |
| (C2×#10597845)⋊C8 | 2 |
| #23757266 | 2 |
| #1929 | 157 |