Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
332 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#19097779 | C2 | semidirect |
| 3. #23757272 | C2 | semidirect |
| 4. C2×#19097691 | C2 | semidirect |
| 5. C2×#19097687 | C2 | semidirect |
| 6. #23757037 | C2 | semidirect |
| 7. #343×C157 | C2 | semidirect |
| 11. #19097799 | C4 | semidirect |
| 123. C157 | #1907 | semidirect |
| 130. #343 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| C2×#19097779 | 2 |
| #23757272 | 2 |
| C2×#19097691 | 2 |
| C2×#19097687 | 2 |
| #23757037 | 2 |
| #343×C157 | 2 |
| #1907 | 157 |