Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23757332 | C2 | semidirect |
| 3. #23757328 | C2 | semidirect |
| 4. #23757301 | C2 | semidirect |
| 6. C2×#19097682 | C2 | semidirect |
| 7. C4×M16×C157 | C2 | semidirect |
| 77. C157 | #2923 | semidirect |
| 84. C4×M16 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578954 | 2 |
| #23757332 | 2 |
| #23757328 | 2 |
| #23757301 | 2 |
| #23757241 | 2 |
| C2×#19097682 | 2 |
| C4×M16×C157 | 2 |
| #2923 | 157 |