Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19097770 | C2 | semidirect |
| 3. #23757567 | C2 | semidirect |
| 4. #23757562 | C2 | semidirect |
| 5. #23757557 | C2 | semidirect |
| 6. #23757552 | C2 | semidirect |
| 7. #23757316 | C2 | semidirect |
| 8. #23757296 | C2 | semidirect |
| 11. #428×C157 | C2 | semidirect |
| 44. #14578954 | Q8 | semidirect |
| 87. Dic314 | C2×Q8 | semidirect |
| 89. D628 | C2×Q8 | semidirect |
| 138. C157 | #3079 | semidirect |
| 147. #428 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097770 | 2 |
| #23757741 | 2 |
| #23757567 | 2 |
| #23757562 | 2 |
| #23757557 | 2 |
| #23757552 | 2 |
| #23757316 | 2 |
| #23757296 | 2 |
| #23757275 | 2 |
| #23757272 | 2 |
| #428×C157 | 2 |
| #3079 | 157 |