Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. C2×#15692302 | C2 | semidirect |
| 2. #20265977 | C2 | semidirect |
| 3. #20265975 | C2 | semidirect |
| 4. #20265753 | C2 | semidirect |
| 5. #20265361 | C2 | semidirect |
| 6. #20265351 | C2 | semidirect |
| 7. #20265195 | C2 | semidirect |
| 8. C2×#15692173 | C2 | semidirect |
| 9. #421×C101 | C2 | semidirect |
| 23. #15692288 | C22 | semidirect |
| 25. #15692285 | C22 | semidirect |
| 27. #15692283 | C22 | semidirect |
| 29. #15692280 | C22 | semidirect |
| 33. #15692255 | C22 | semidirect |
| 34. #15692243 | C22 | semidirect |
| 37. #15692183 | C22 | semidirect |
| 38. #15692173 | C22 | semidirect |
| 42. #104×C101 | C22 | semidirect |
| 186. C101 | #3020 | semidirect |
| 194. #421 | D101 | semidirect |
| 227. #104 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| #20265977 | 2 |
| #20265975 | 2 |
| #20265753 | 2 |
| #20265361 | 2 |
| #20265351 | 2 |
| #20265195 | 2 |
| C2×#15692173 | 2 |
| #421×C101 | 2 |
| #3020 | 101 |