Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23758002 | C2 | semidirect |
| 3. #23757636 | C2 | semidirect |
| 4. #23757620 | C2 | semidirect |
| 5. #23757572 | C2 | semidirect |
| 6. #23757553 | C2 | semidirect |
| 7. #23757473 | C2 | semidirect |
| 8. #23757471 | C2 | semidirect |
| 9. #23757403 | C2 | semidirect |
| 10. #23757376 | C2 | semidirect |
| 11. C4×SD16×C157 | C2 | semidirect |
| 90. Q8×C157 | #41 | semidirect |
| 124. C157 | #3368 | semidirect |
| 136. C4×SD16 | D157 | semidirect |
| 204. Q8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758002 | 2 |
| #23757944 | 2 |
| #23757636 | 2 |
| #23757620 | 2 |
| #23757572 | 2 |
| #23757553 | 2 |
| #23757473 | 2 |
| #23757471 | 2 |
| #23757403 | 2 |
| #23757376 | 2 |
| C4×SD16×C157 | 2 |
| #3368 | 157 |