Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. #20265830 | C2 | semidirect |
| 2. D4×D404 | C2 | semidirect |
| 3. #20265525 | C2 | semidirect |
| 4. #20265492 | C2 | semidirect |
| 5. #20265414 | C2 | semidirect |
| 6. #20265373 | C2 | semidirect |
| 7. #20265312 | C2 | semidirect |
| 8. C4×#13108059 | C2 | semidirect |
| 9. #20265242 | C2 | semidirect |
| 10. #102×D101 | C2 | semidirect |
| 11. #474×C101 | C2 | semidirect |
| 15. C2×D808 | C22 | semidirect |
| 17. C2×C8×D101 | C22 | semidirect |
| 22. #15692230 | C22 | semidirect |
| 26. C4×D404 | C22 | semidirect |
| 27. C4⋊C4×D101 | C22 | semidirect |
| 28. #15692188 | C22 | semidirect |
| 29. #15692177 | C22 | semidirect |
| 31. #15692175 | C22 | semidirect |
| 32. #15692175 | C22 | semidirect |
| 33. #15692175 | C22 | semidirect |
| 34. #15692167 | C22 | semidirect |
| 35. C4×#11717579 | C22 | semidirect |
| 36. C4⋊Q8×C101 | C22 | semidirect |
| 38. #107×C101 | C22 | semidirect |
| 39. C4⋊C8×C101 | C22 | semidirect |
| 87. D4×C101 | #41 | semidirect |
| 105. D404 | D8 | semidirect |
| 143. C101 | #3294 | semidirect |
| 148. #474 | D101 | semidirect |
| 161. C4⋊Q8 | C2×D101 | semidirect |
| 174. #107 | C2×D101 | semidirect |
| 175. C4⋊C8 | C2×D101 | semidirect |
| 240. D4 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265830 | 2 |
| D4×D404 | 2 |
| #20265525 | 2 |
| #20265492 | 2 |
| #20265414 | 2 |
| #20265373 | 2 |
| #20265312 | 2 |
| C4×#13108059 | 2 |
| #20265242 | 2 |
| #102×D101 | 2 |
| #474×C101 | 2 |
| #3294 | 101 |