Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. C2×C4×#13181884 | C2 | semidirect |
| 4. (C2×#13181884)⋊C4 | C2 | semidirect |
| 7. C22×#13181884 | C4 | semidirect |
| 11. C22⋊#13181884 | C4 | semidirect |
| 15. C22⋊Dic433 | C4 | semidirect |
| 16. #20294074 | C4 | semidirect |
| 17. C22⋊C4×C433 | C4 | semidirect |
| 24. C2×#13181884 | C2×C4 | semidirect |
| 32. C2×Dic433 | C2×C4 | semidirect |
| 36. C2×C4×C433 | C2×C4 | semidirect |
| 38. C22×C433 | C42 | semidirect |
| 44. C2×D433 | C42 | semidirect |
| 51. #13181884 | C22⋊C4 | direct (N × H) |
| 61. C433 | C4×C22⋊C4 | semidirect |
| 78. C22⋊C4 | #13181884 | direct (N × H) |
| 98. C2×C4 | C2×#13181884 | semidirect |
| 109. C22 | C4×#13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13181884 | 2 |
| C2×C22⋊#13181884 | 2 |
| C2×C4×#13181884 | 2 |
| (C2×#13181884)⋊C4 | 2 |
| C22⋊C4×D433 | 2 |
| C4×C22⋊C4 | 433 |