Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
384 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#19097683 | C2 | semidirect |
| 3. C2×#19097682 | C2 | semidirect |
| 4. C2×C4⋊C8×C157 | C2 | semidirect |
| 27. C2×#11929434 | D4 | semidirect |
| 79. C157 | #1955 | semidirect |
| 82. C2×C4⋊C8 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D628 | 2 |
| C2×#19097683 | 2 |
| C2×#19097682 | 2 |
| C2×C4⋊C8×C157 | 2 |
| #1955 | 157 |