Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757996 | C2 | semidirect |
| 2. #23757635 | C2 | semidirect |
| 3. #23757625 | C2 | semidirect |
| 4. #23757565 | C2 | semidirect |
| 5. #23757550 | C2 | semidirect |
| 7. #23757478 | C2 | semidirect |
| 8. #23757404 | C2 | semidirect |
| 9. #23757373 | C2 | semidirect |
| 11. D4×Q8×C157 | C2 | semidirect |
| 122. C157 | #3367 | semidirect |
| 125. D4×Q8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| #23757635 | 2 |
| #23757625 | 2 |
| #23757565 | 2 |
| #23757550 | 2 |
| #23757488 | 2 |
| #23757478 | 2 |
| #23757404 | 2 |
| #23757373 | 2 |
| C4×#14578939 | 2 |
| D4×Q8×C157 | 2 |
| #3367 | 157 |