Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊Dic317 | C2 | semidirect |
| 4. #23778687 | C2 | semidirect |
| 5. C2×C4⋊C4×C317 | C2 | semidirect |
| 11. C2×C4×D317 | C4 | semidirect |
| 51. C2×D317 | C4⋊C4 | semidirect |
| 53. C4×C317 | C22⋊C4 | semidirect |
| 64. C317 | #380 | semidirect |
| 68. C2×C4⋊C4 | D317 | semidirect |
| 120. C4 | #19099551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D317 | 2 |
| C2×C4⋊Dic317 | 2 |
| C2×#19099551 | 2 |
| #23778687 | 2 |
| C2×C4⋊C4×C317 | 2 |
| #380 | 317 |