Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
226 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23778770 | C2 | direct (N × H) |
| 49. C2×C317 | #125 | semidirect |
| 53. C317 | C2×#125 | semidirect |
| 103. C2 | #23778770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778770 | 2 |
| C2×C4⋊Dic317 | 2 |
| C2×#19099553 | 2 |
| C2×C4×Dic317 | 2 |
| C2×C4⋊C4×C317 | 2 |
| C2×#125 | 317 |