Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #23758001 | C2 | semidirect |
| 3. #23757624 | C2 | semidirect |
| 4. #23757622 | C2 | semidirect |
| 5. #23757558 | C2 | semidirect |
| 6. #23757557 | C2 | semidirect |
| 9. C8×Dic314 | C2 | semidirect |
| 78. Dic314 | SD16 | semidirect |
| 118. C157 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758001 | 2 |
| D4×Dic314 | 2 |
| #23757624 | 2 |
| #23757622 | 2 |
| #23757558 | 2 |
| #23757557 | 2 |
| #23757478 | 2 |
| #23757476 | 2 |
| C8×Dic314 | 2 |
| #23757364 | 2 |
| C4×SD16×C157 | 2 |
| #3359 | 157 |