Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15692262 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265428 | C2 | semidirect |
| 5. #20265425 | C2 | semidirect |
| 6. #20265411 | C2 | semidirect |
| 7. #20265408 | C2 | semidirect |
| 8. #20265217 | C2 | semidirect |
| 9. #20265173 | C2 | semidirect |
| 10. C2×#15692175 | C2 | semidirect |
| 11. #537×C101 | C2 | semidirect |
| 18. C2×#13108058 | C22 | semidirect |
| 20. C22×#11717579 | C22 | semidirect |
| 27. #15692188 | C22 | semidirect |
| 28. #15692186 | C22 | semidirect |
| 29. #15692179 | C22 | semidirect |
| 30. #15692179 | C22 | semidirect |
| 31. #15692176 | C22 | semidirect |
| 32. #15692176 | C22 | semidirect |
| 38. C22⋊Q8×C101 | C22 | semidirect |
| 41. #121×C101 | C22 | semidirect |
| 53. #13108058 | D4 | semidirect |
| 152. C101 | #3062 | semidirect |
| 155. #537 | D101 | semidirect |
| 178. C22⋊Q8 | C2×D101 | semidirect |
| 183. #121 | 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×#15692262 | 2 |
| #20265741 | 2 |
| #20265428 | 2 |
| #20265425 | 2 |
| #20265411 | 2 |
| #20265408 | 2 |
| #20265217 | 2 |
| #20265173 | 2 |
| C2×#15692175 | 2 |
| #537×C101 | 2 |
| #3062 | 101 |