Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 91 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×#19097702 | C2 | semidirect |
| 2. C2×#19097695 | C2 | semidirect |
| 3. C2×#19097695 | C2 | semidirect |
| 6. #23757035 | C2 | semidirect |
| 129. C157 | #2035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097702 | 2 |
| C2×#19097695 | 2 |
| C2×C22⋊#11929434 | 2 |
| #23757133 | 2 |
| #23757035 | 2 |
| C2×C22⋊Q8×C157 | 2 |
| #2035 | 157 |