Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20265336 | C2 | semidirect |
| 5. #20265326 | C2 | semidirect |
| 6. #20265182 | C2 | semidirect |
| 7. #20265174 | C2 | semidirect |
| 8. #20265143 | C2 | semidirect |
| 9. C22×SD16×C101 | C2 | semidirect |
| 20. C2×#13108064 | C22 | semidirect |
| 21. C2×#13108061 | C22 | semidirect |
| 22. C2×#13108058 | C22 | semidirect |
| 26. #15692231 | C22 | semidirect |
| 27. #15692214 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 29. #15692177 | C22 | semidirect |
| 30. #15692176 | C22 | semidirect |
| 31. #15692167 | C22 | semidirect |
| 32. C22×Q8×C101 | C22 | semidirect |
| 35. C2×SD16×C101 | C22 | semidirect |
| 36. C22×C8×C101 | C22 | semidirect |
| 147. C101 | #3009 | semidirect |
| 150. C22×SD16 | D101 | semidirect |
| 163. C22×Q8 | C2×D101 | semidirect |
| 172. C2×SD16 | C2×D101 | semidirect |
| 174. C22×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692300 | 2 |
| C2×#15692286 | 2 |
| #20265751 | 2 |
| #20265336 | 2 |
| #20265326 | 2 |
| #20265182 | 2 |
| #20265174 | 2 |
| #20265143 | 2 |
| C22×SD16×C101 | 2 |
| #3009 | 101 |