Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
428 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 10. #19097763 | C4 | semidirect |
| 98. C157 | #2336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097763 | 2 |
| #23757168 | 2 |
| #23757158 | 2 |
| #23757157 | 2 |
| #23757156 | 2 |
| #23757154 | 2 |
| #23757141 | 2 |
| C4×#14578933 | 2 |
| C4×C4⋊C4×C157 | 2 |
| #2336 | 157 |