Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23757993 | C2 | semidirect |
| 2. D4×Dic314 | C2 | semidirect |
| 3. #23757631 | C2 | semidirect |
| 4. #23757624 | C2 | semidirect |
| 5. #23757567 | C2 | semidirect |
| 6. #23757553 | C2 | semidirect |
| 8. #23757478 | C2 | semidirect |
| 9. #23757403 | C2 | semidirect |
| 10. #23757370 | C2 | semidirect |
| 122. C157 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757993 | 2 |
| D4×Dic314 | 2 |
| #23757631 | 2 |
| #23757624 | 2 |
| #23757567 | 2 |
| #23757553 | 2 |
| #23757486 | 2 |
| #23757478 | 2 |
| #23757403 | 2 |
| #23757370 | 2 |
| C4×D8×C157 | 2 |
| #3367 | 157 |