Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 9. C4⋊#13181884 | C4 | semidirect |
| 11. C4×#13181884 | C4 | semidirect |
| 14. C4⋊Dic433 | C4 | semidirect |
| 15. #20294076 | C4 | semidirect |
| 16. C4⋊C4×C433 | C4 | semidirect |
| 44. #13181884 | C4⋊C4 | direct (N × H) |
| 46. C4×C433 | C42 | semidirect |
| 48. Dic433 | C42 | semidirect |
| 56. C433 | C4×C4⋊C4 | semidirect |
| 71. C4⋊C4 | #13181884 | direct (N × H) |
| 105. C4 | C4×#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 |
| C4⋊C4×D433 | 2 |
| C4×C4⋊C4 | 433 |