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×#15692288 | C2 | semidirect |
| 3. C2×#15692285 | C2 | semidirect |
| 4. #20265753 | C2 | semidirect |
| 5. #20265361 | C2 | semidirect |
| 6. #20265356 | C2 | semidirect |
| 7. #20265195 | C2 | semidirect |
| 8. #20265159 | C2 | semidirect |
| 9. #421×C101 | C2 | semidirect |
| 22. C22×Dic202 | C22 | semidirect |
| 24. #15692288 | C22 | semidirect |
| 26. #15692285 | C22 | semidirect |
| 31. C2×#13108058 | C22 | semidirect |
| 32. #15692255 | C22 | semidirect |
| 33. #15692243 | C22 | semidirect |
| 36. #15692183 | C22 | semidirect |
| 37. #15692173 | C22 | semidirect |
| 38. #15692171 | C22 | semidirect |
| 40. C2×M16×C101 | C22 | semidirect |
| 41. #117×C101 | C22 | semidirect |
| 42. #104×C101 | C22 | semidirect |
| 193. C101 | #3022 | semidirect |
| 201. #421 | D101 | semidirect |
| 226. C2×M16 | C2×D101 | semidirect |
| 231. #117 | C2×D101 | semidirect |
| 233. #104 | 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×#15692288 | 2 |
| C2×#15692285 | 2 |
| #20265753 | 2 |
| #20265361 | 2 |
| #20265356 | 2 |
| #20265195 | 2 |
| #20265159 | 2 |
| #421×C101 | 2 |
| #3022 | 101 |