Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #23757565 | C2 | semidirect |
| 3. #23757560 | C2 | semidirect |
| 4. #23757555 | C2 | semidirect |
| 5. #23757550 | C2 | semidirect |
| 6. #23757313 | C2 | semidirect |
| 7. #23757297 | C2 | semidirect |
| 9. C2×C4⋊Q8×C157 | C2 | semidirect |
| 36. #14578954 | Q8 | semidirect |
| 72. Dic314 | C2×Q8 | semidirect |
| 74. D628 | C2×Q8 | semidirect |
| 121. C157 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14578954 | 2 |
| #23757565 | 2 |
| #23757560 | 2 |
| #23757555 | 2 |
| #23757550 | 2 |
| #23757313 | 2 |
| #23757297 | 2 |
| #23757272 | 2 |
| C2×C4⋊Q8×C157 | 2 |
| #3079 | 157 |