Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×#20294107 | C2 | semidirect |
| 2. C2×C4×#13181884 | C2 | semidirect |
| 3. #28357285 | C2 | direct (N × H) |
| 7. #20294107 | C22 | semidirect |
| 10. C4×#13181884 | C22 | semidirect |
| 13. #20294098 | C4 | semidirect |
| 16. C2×D1732 | C4 | semidirect |
| 19. C2×Q8×C433 | C4 | semidirect |
| 28. D1732 | C2×C4 | semidirect |
| 37. Q8×C433 | C2×C4 | semidirect |
| 52. C2×C433 | #104 | semidirect |
| 57. C433 | C2×#104 | semidirect |
| 67. C2×Q8 | #13181884 | semidirect |
| 81. Q8 | C2×#13181884 | semidirect |
| 113. C2 | #28357285 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294107 | 2 |
| C2×C4×#13181884 | 2 |
| #28357285 | 2 |
| C2×#20294098 | 2 |
| C2×#104 | 433 |