Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
186 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 186 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 |
|---|---|---|
| 9. C2×Dic866 | C4 | semidirect |
| 10. C2×Dic866 | C4 | semidirect |
| 15. C2×Q8×C433 | C4 | semidirect |
| 20. C2×#13181884 | Q8 | semidirect |
| 49. C433 | #391 | semidirect |
| 59. C2×Q8 | #13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13181884 | 2 |
| C2×C4×#13181884 | 2 |
| (C2×#13181884)⋊C4 | 2 |
| C2×Q8×D433 | 2 |
| #391 | 433 |