Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23757927 | C2 | semidirect |
| 2. #23757669 | C2 | semidirect |
| 3. #23757597 | C2 | semidirect |
| 4. #23757589 | C2 | semidirect |
| 5. #23757560 | C2 | semidirect |
| 6. #23757553 | C2 | semidirect |
| 7. #23757524 | C2 | semidirect |
| 8. C4×#14578939 | C2 | semidirect |
| 9. #23757351 | C2 | semidirect |
| 10. #23757316 | C2 | semidirect |
| 11. #555×C157 | C2 | semidirect |
| 85. #11929434 | #41 | semidirect |
| 127. C157 | #3354 | semidirect |
| 129. #555 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757927 | 2 |
| #23757669 | 2 |
| #23757597 | 2 |
| #23757589 | 2 |
| #23757560 | 2 |
| #23757553 | 2 |
| #23757524 | 2 |
| C4×#14578939 | 2 |
| #23757351 | 2 |
| #23757316 | 2 |
| #555×C157 | 2 |
| #3354 | 157 |