Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D433 | C2 | semidirect |
| 3. #28357249 | C2 | direct (N × H) |
| 4. C2×Dic1732 | C2 | semidirect |
| 5. C2×#20294087 | C2 | semidirect |
| 6. C2×#20294085 | C2 | semidirect |
| 7. C2×#20294080 | C2 | semidirect |
| 8. C2×SD16×C433 | C2 | semidirect |
| 15. Q8×D433 | C22 | semidirect |
| 20. Dic1732 | C22 | semidirect |
| 21. #20294087 | C22 | semidirect |
| 22. #20294085 | C22 | semidirect |
| 23. #20294080 | C22 | semidirect |
| 27. SD16×C433 | C22 | semidirect |
| 64. C2×C433 | #137 | semidirect |
| 67. C433 | C2×#137 | semidirect |
| 75. C2×SD16 | D433 | semidirect |
| 93. SD16 | C2×D433 | semidirect |
| 133. C2 | #28357249 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294096 | 2 |
| C2×Q8×D433 | 2 |
| #28357249 | 2 |
| C2×Dic1732 | 2 |
| C2×#20294087 | 2 |
| C2×#20294085 | 2 |
| C2×#20294080 | 2 |
| C2×SD16×C433 | 2 |
| C2×#137 | 433 |