Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 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. D4×#13181884 | C2 | semidirect |
| 2. #28357299 | C2 | semidirect |
| 3. C2×C22⋊#13181884 | C2 | semidirect |
| 5. C22×#13181884 | C22 | semidirect |
| 6. C4⋊#13181884 | C22 | semidirect |
| 8. C22⋊#13181884 | C22 | semidirect |
| 9. C4×#13181884 | C22 | semidirect |
| 11. C2×D1732 | C4 | semidirect |
| 12. C2×C22⋊D433 | C4 | semidirect |
| 13. D4×D433 | C4 | semidirect |
| 16. C2×D4×C433 | C4 | semidirect |
| 20. C22×D433 | C2×C4 | semidirect |
| 21. C22×D433 | 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 |
| 29. C23×C433 | C2×C4 | semidirect |
| 30. D4×C433 | C2×C4 | semidirect |
| 31. C2×C4×C433 | C2×C4 | semidirect |
| 51. C433 | #518 | semidirect |
| 62. C2×D4 | #13181884 | semidirect |
| 74. C23 | C2×#13181884 | semidirect |
| 77. D4 | C2×#13181884 | semidirect |
| 83. C2×C4 | C2×#13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#13181884 | 2 |
| #28357299 | 2 |
| C2×C22⋊#13181884 | 2 |
| C2×D4×D433 | 2 |
| #518 | 433 |