Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 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. Q8×#13181884 | C2 | semidirect |
| 2. D4×#13181884 | C2 | semidirect |
| 3. #28357299 | C2 | semidirect |
| 4. C2×C4⋊#13181884 | C2 | semidirect |
| 12. #20294098 | C4 | semidirect |
| 13. #20294097 | C4 | semidirect |
| 14. #20294096 | C4 | semidirect |
| 18. #41×C433 | C4 | semidirect |
| 23. Dic866 | C2×C4 | semidirect |
| 24. D1732 | C2×C4 | semidirect |
| 25. C22⋊D433 | C2×C4 | semidirect |
| 26. C2×Dic433 | C2×C4 | semidirect |
| 27. C4×D433 | C2×C4 | semidirect |
| 28. C4×D433 | C2×C4 | semidirect |
| 31. Q8×C433 | C2×C4 | semidirect |
| 32. D4×C433 | C2×C4 | semidirect |
| 33. C2×C4×C433 | C2×C4 | semidirect |
| 50. C433 | #520 | semidirect |
| 60. #41 | #13181884 | semidirect |
| 72. Q8 | C2×#13181884 | semidirect |
| 75. D4 | C2×#13181884 | semidirect |
| 84. C2×C4 | C2×#13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13181884 | 2 |
| D4×#13181884 | 2 |
| #28357299 | 2 |
| C2×C4⋊#13181884 | 2 |
| #41×D433 | 2 |
| #520 | 433 |