Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
170 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20294076 | C4 | semidirect |
| 55. Dic433 | C4⋊C4 | semidirect |
| 63. C433 | #389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294076 | 2 |
| C2×C4×Dic433 | 2 |
| #28357127 | 2 |
| C2×C4⋊C4×C433 | 2 |
| #389 | 433 |