Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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×#15692286 | C2 | semidirect |
| 3. #20265751 | C2 | semidirect |
| 4. #20265358 | C2 | semidirect |
| 5. #20265353 | C2 | semidirect |
| 6. #20265194 | C2 | semidirect |
| 7. #20265193 | C2 | semidirect |
| 8. #20265159 | C2 | semidirect |
| 9. C2×#137×C101 | C2 | semidirect |
| 23. #15692286 | C22 | semidirect |
| 26. C2×#13108058 | C22 | semidirect |
| 27. #15692253 | C22 | semidirect |
| 28. #15692244 | C22 | semidirect |
| 31. #15692214 | C22 | semidirect |
| 32. #15692182 | C22 | semidirect |
| 33. #15692181 | C22 | semidirect |
| 34. #15692173 | C22 | semidirect |
| 35. #15692171 | C22 | semidirect |
| 37. C22×Q8×C101 | C22 | semidirect |
| 39. #137×C101 | C22 | semidirect |
| 42. C2×M16×C101 | C22 | semidirect |
| 193. C101 | #3022 | semidirect |
| 196. C2×#137 | D101 | semidirect |
| 216. C22×Q8 | C2×D101 | semidirect |
| 220. #137 | C2×D101 | semidirect |
| 226. C2×M16 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| C2×#15692286 | 2 |
| #20265751 | 2 |
| #20265358 | 2 |
| #20265353 | 2 |
| #20265194 | 2 |
| #20265193 | 2 |
| #20265159 | 2 |
| C2×#137×C101 | 2 |
| #3022 | 101 |