Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19097804 | C2 | semidirect |
| 3. #23757849 | C2 | semidirect |
| 4. #23757753 | C2 | semidirect |
| 5. #23757496 | C2 | semidirect |
| 6. #23757489 | C2 | semidirect |
| 7. #23757484 | C2 | semidirect |
| 8. #23757479 | C2 | semidirect |
| 9. #23757275 | C2 | semidirect |
| 10. C2×#19097696 | C2 | semidirect |
| 11. #424×C157 | C2 | semidirect |
| 146. C157 | #3046 | semidirect |
| 156. #424 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097793 | 2 |
| #23757849 | 2 |
| #23757753 | 2 |
| #23757496 | 2 |
| #23757489 | 2 |
| #23757484 | 2 |
| #23757479 | 2 |
| #23757275 | 2 |
| C2×#19097696 | 2 |
| #424×C157 | 2 |
| #3046 | 157 |