Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D628 | C2 | semidirect |
| 2. #23757632 | C2 | semidirect |
| 3. #23757623 | C2 | semidirect |
| 4. #23757568 | C2 | semidirect |
| 5. #23757553 | C2 | semidirect |
| 7. #23757475 | C2 | semidirect |
| 8. #23757404 | C2 | semidirect |
| 9. #23757371 | C2 | semidirect |
| 11. #556×C157 | C2 | semidirect |
| 122. C157 | #3367 | semidirect |
| 124. #556 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D628 | 2 |
| #23757632 | 2 |
| #23757623 | 2 |
| #23757568 | 2 |
| #23757553 | 2 |
| #23757485 | 2 |
| #23757475 | 2 |
| #23757404 | 2 |
| #23757371 | 2 |
| C4×#14578939 | 2 |
| #556×C157 | 2 |
| #3367 | 157 |