Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 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. C2×C4⋊Dic317 | C2 | semidirect |
| 2. C2×#19099553 | C2 | semidirect |
| 3. C2×#19099553 | C2 | semidirect |
| 6. #23778687 | C2 | semidirect |
| 75. C317 | #396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic317 | 2 |
| C2×#19099553 | 2 |
| C2×C22⋊Dic317 | 2 |
| #23778687 | 2 |
| C2×C22⋊C4×C317 | 2 |
| #396 | 317 |