Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 14. C4⋊Dic317 | C4 | semidirect |
| 15. #19099553 | C4 | semidirect |
| 16. C4⋊C4×C317 | C4 | semidirect |
| 46. C4×C317 | C4⋊C4 | semidirect |
| 48. Dic317 | C4⋊C4 | semidirect |
| 56. C317 | #389 | semidirect |
| 72. C4⋊C4 | #11929639 | semidirect |
| 105. C4 | C4⋊#11929639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11929639 | 2 |
| C2×C4×#11929639 | 2 |
| (C2×#11929639)⋊C4 | 2 |
| C4⋊C4×D317 | 2 |
| #389 | 317 |