Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#19097794 | C2 | semidirect |
| 2. C2×#19097714 | C2 | semidirect |
| 3. C2×D2512 | C2 | semidirect |
| 4. #23757510 | C2 | semidirect |
| 5. #23757073 | C2 | semidirect |
| 6. #23757052 | C2 | semidirect |
| 7. #358×C157 | C2 | semidirect |
| 35. D1256 | D4 | semidirect |
| 43. Q16×C157 | D4 | semidirect |
| 89. C157 | #2186 | semidirect |
| 95. #358 | D157 | semidirect |
| 123. Q16 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×#19097714 | 2 |
| C2×D2512 | 2 |
| #23757510 | 2 |
| #23757073 | 2 |
| #23757052 | 2 |
| #358×C157 | 2 |
| #2186 | 157 |