Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265887 | C2 | semidirect |
| 3. #20265523 | C2 | semidirect |
| 4. #20265494 | C2 | semidirect |
| 5. #20265468 | C2 | semidirect |
| 6. #20265403 | C2 | semidirect |
| 7. #20265326 | C2 | semidirect |
| 8. C4×#13108061 | C2 | semidirect |
| 9. #20265242 | C2 | semidirect |
| 10. #102×D101 | C2 | semidirect |
| 11. #460×C101 | C2 | semidirect |
| 15. C2×C8×D101 | C22 | semidirect |
| 16. #15692255 | C22 | semidirect |
| 19. #15692231 | C22 | semidirect |
| 26. C4⋊C4×D101 | C22 | semidirect |
| 27. #15692187 | C22 | semidirect |
| 28. #15692186 | C22 | semidirect |
| 29. #15692179 | C22 | semidirect |
| 31. #15692176 | C22 | semidirect |
| 32. #15692176 | C22 | semidirect |
| 34. #15692167 | C22 | semidirect |
| 35. C4×#11717579 | C22 | semidirect |
| 36. C2×SD16×C101 | C22 | semidirect |
| 38. C4×Q8×C101 | C22 | semidirect |
| 39. C4⋊C8×C101 | C22 | semidirect |
| 40. #102×C101 | C22 | semidirect |
| 100. D404 | SD16 | semidirect |
| 137. C101 | #3295 | semidirect |
| 144. #460 | D101 | semidirect |
| 152. C2×SD16 | C2×D101 | semidirect |
| 162. C4×Q8 | C2×D101 | semidirect |
| 169. C4⋊C8 | C2×D101 | semidirect |
| 175. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265887 | 2 |
| #20265812 | 2 |
| #20265523 | 2 |
| #20265494 | 2 |
| #20265468 | 2 |
| #20265403 | 2 |
| #20265326 | 2 |
| C4×#13108061 | 2 |
| #20265242 | 2 |
| #102×D101 | 2 |
| #460×C101 | 2 |
| #3295 | 101 |