Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D157 | C2 | semidirect |
| 3. #23757567 | C2 | semidirect |
| 4. #23757561 | C2 | semidirect |
| 5. #23757559 | C2 | semidirect |
| 6. #23757555 | C2 | semidirect |
| 7. #23757553 | C2 | semidirect |
| 8. #23757314 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 11. #474×C157 | C2 | semidirect |
| 44. #14578953 | Q8 | semidirect |
| 86. Dic314 | C2×Q8 | semidirect |
| 105. D4×C157 | C2×Q8 | semidirect |
| 137. C157 | #3079 | semidirect |
| 146. #474 | D157 | semidirect |
| 229. D4 | Q8×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D157 | 2 |
| C4×#14578953 | 2 |
| #23757567 | 2 |
| #23757561 | 2 |
| #23757559 | 2 |
| #23757555 | 2 |
| #23757553 | 2 |
| #23757314 | 2 |
| #23757295 | 2 |
| #23757271 | 2 |
| #474×C157 | 2 |
| #3079 | 157 |