Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15692280 | C2 | semidirect |
| 2. C2×#15692261 | C2 | semidirect |
| 3. #20265755 | C2 | semidirect |
| 4. #20265746 | C2 | semidirect |
| 5. #20265429 | C2 | semidirect |
| 6. #20265426 | C2 | semidirect |
| 7. #20265412 | C2 | semidirect |
| 8. #20265409 | C2 | semidirect |
| 9. #20265220 | C2 | semidirect |
| 10. C2×#15692177 | C2 | semidirect |
| 11. #416×C101 | C2 | semidirect |
| 19. C2×#13108057 | C22 | semidirect |
| 20. C2×C8×D101 | C22 | semidirect |
| 24. #15692231 | C22 | semidirect |
| 29. #15692226 | C22 | semidirect |
| 32. #15692188 | C22 | semidirect |
| 33. #15692186 | C22 | semidirect |
| 39. #103×C101 | C22 | semidirect |
| 40. #103×C101 | C22 | semidirect |
| 41. #102×C101 | C22 | semidirect |
| 42. #102×C101 | C22 | semidirect |
| 60. #13108058 | D4 | semidirect |
| 152. C101 | #3062 | semidirect |
| 162. #416 | D101 | semidirect |
| 189. #103 | C2×D101 | semidirect |
| 190. #103 | C2×D101 | semidirect |
| 193. #102 | C2×D101 | semidirect |
| 194. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692280 | 2 |
| C2×#15692261 | 2 |
| #20265755 | 2 |
| #20265746 | 2 |
| #20265429 | 2 |
| #20265426 | 2 |
| #20265412 | 2 |
| #20265409 | 2 |
| #20265220 | 2 |
| C2×#15692177 | 2 |
| #416×C101 | 2 |
| #3062 | 101 |