Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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. C8×Dic314 | C2 | semidirect |
| 4. #23757026 | C2 | semidirect |
| 5. #23757005 | C2 | semidirect |
| 7. #322×C157 | C2 | semidirect |
| 43. Dic314 | M16 | semidirect |
| 77. C157 | #1588 | semidirect |
| 85. #322 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic314 | 2 |
| C4×#14578943 | 2 |
| #23757352 | 2 |
| #23757026 | 2 |
| #23757005 | 2 |
| #23757002 | 2 |
| #322×C157 | 2 |
| #1588 | 157 |