Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20265991 | C2 | semidirect |
| 2. #20265989 | C2 | semidirect |
| 3. #20265979 | C2 | semidirect |
| 4. #20265561 | C2 | semidirect |
| 5. #20265453 | C2 | semidirect |
| 6. #20265448 | C2 | semidirect |
| 7. #20265440 | C2 | semidirect |
| 8. #20265356 | C2 | semidirect |
| 9. #20265351 | C2 | semidirect |
| 10. #20265295 | C2 | semidirect |
| 11. #443×C101 | C2 | semidirect |
| 12. #15692302 | C22 | semidirect |
| 16. #15692285 | C22 | semidirect |
| 19. #15692283 | C22 | semidirect |
| 26. C2×Dic404 | C22 | semidirect |
| 29. C2×#13108063 | C22 | semidirect |
| 33. #15692261 | C22 | semidirect |
| 34. #15692243 | C22 | semidirect |
| 35. #15692191 | C22 | semidirect |
| 37. #15692183 | C22 | semidirect |
| 38. #15692173 | C22 | semidirect |
| 39. #15692171 | C22 | semidirect |
| 41. #131×C101 | C22 | semidirect |
| 42. #108×C101 | C22 | semidirect |
| 43. #104×C101 | C22 | semidirect |
| 44. C4×C8×C101 | C22 | semidirect |
| 150. C101 | #3290 | semidirect |
| 161. #443 | D101 | semidirect |
| 185. #131 | C2×D101 | semidirect |
| 188. #108 | C2×D101 | semidirect |
| 191. #104 | C2×D101 | semidirect |
| 194. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265991 | 2 |
| #20265989 | 2 |
| #20265979 | 2 |
| #20265561 | 2 |
| #20265453 | 2 |
| #20265448 | 2 |
| #20265440 | 2 |
| #20265356 | 2 |
| #20265351 | 2 |
| #20265295 | 2 |
| #443×C101 | 2 |
| #3290 | 101 |