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. #23757996 | C2 | semidirect |
| 2. Q8×D628 | C2 | semidirect |
| 3. #23757633 | C2 | semidirect |
| 4. #23757624 | C2 | semidirect |
| 5. #23757569 | C2 | semidirect |
| 6. #23757554 | C2 | semidirect |
| 8. #23757479 | C2 | semidirect |
| 9. #23757375 | C2 | semidirect |
| 11. #446×C157 | C2 | semidirect |
| 122. C157 | #3367 | semidirect |
| 132. #446 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757996 | 2 |
| Q8×D628 | 2 |
| #23757633 | 2 |
| #23757624 | 2 |
| #23757569 | 2 |
| #23757554 | 2 |
| #23757489 | 2 |
| #23757479 | 2 |
| #23757375 | 2 |
| C4×D1256 | 2 |
| #446×C157 | 2 |
| #3367 | 157 |