Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #23757402 | C2 | semidirect |
| 3. #23757400 | C2 | semidirect |
| 33. C2×#11929434 | Q8 | semidirect |
| 83. C157 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757826 | 2 |
| #23757402 | 2 |
| #23757400 | 2 |
| #23757299 | 2 |
| #23757296 | 2 |
| #23757231 | 2 |
| #23757229 | 2 |
| C2×#19097681 | 2 |
| #424×C157 | 2 |
| #2961 | 157 |