Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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. #28357299 | C2 | direct (N × H) |
| 2. C2×C4⋊#13181884 | C2 | semidirect |
| 4. C2×C4×#13181884 | C2 | semidirect |
| 7. C4⋊#13181884 | C22 | semidirect |
| 9. C4×#13181884 | C22 | semidirect |
| 11. C22×Dic433 | C4 | semidirect |
| 12. C2×C4×D433 | C4 | semidirect |
| 13. C2×C4×D433 | C4 | semidirect |
| 14. C2×C4×D433 | C4 | semidirect |
| 18. C22×C4×C433 | C4 | semidirect |
| 28. C2×Dic433 | C2×C4 | semidirect |
| 31. C4×D433 | C2×C4 | semidirect |
| 32. C4×D433 | C2×C4 | semidirect |
| 38. C2×C4×C433 | C2×C4 | semidirect |
| 55. C2×C433 | #117 | semidirect |
| 58. D433 | #117 | semidirect |
| 60. C433 | C2×#117 | semidirect |
| 76. C22×C4 | #13181884 | semidirect |
| 99. C2×C4 | C2×#13181884 | semidirect |
| 119. C2 | #28357299 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357299 | 2 |
| C2×C4⋊#13181884 | 2 |
| C2×C22⋊#13181884 | 2 |
| C2×C4×#13181884 | 2 |
| C22×C4×D433 | 2 |
| C2×#117 | 433 |