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. #20265985 | C2 | semidirect |
| 2. #20265979 | C2 | semidirect |
| 3. #20265562 | C2 | semidirect |
| 4. #20265449 | C2 | semidirect |
| 5. #20265447 | C2 | semidirect |
| 6. #20265442 | C2 | semidirect |
| 7. #20265353 | C2 | semidirect |
| 8. #20265350 | C2 | semidirect |
| 9. #20265294 | C2 | semidirect |
| 10. #20265292 | C2 | semidirect |
| 11. #578×C101 | C2 | semidirect |
| 18. #15692280 | C22 | semidirect |
| 23. C2×#13108061 | C22 | semidirect |
| 26. #15692262 | C22 | semidirect |
| 28. #15692244 | C22 | semidirect |
| 29. #15692191 | C22 | semidirect |
| 30. #15692190 | C22 | semidirect |
| 31. #15692182 | C22 | semidirect |
| 32. #15692182 | C22 | semidirect |
| 34. #15692174 | C22 | semidirect |
| 35. #15692171 | C22 | semidirect |
| 36. C8×Dic101 | C22 | semidirect |
| 37. 2−1+4×C101 | C22 | semidirect |
| 39. #137×C101 | C22 | semidirect |
| 43. C2×Q16×C101 | C22 | semidirect |
| 44. #131×C101 | C22 | semidirect |
| 150. C101 | #3290 | semidirect |
| 151. #578 | D101 | semidirect |
| 162. 2−1+4 | C2×D101 | semidirect |
| 167. #137 | C2×D101 | semidirect |
| 178. C2×Q16 | C2×D101 | semidirect |
| 185. #131 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265985 | 2 |
| #20265979 | 2 |
| #20265562 | 2 |
| #20265449 | 2 |
| #20265447 | 2 |
| #20265442 | 2 |
| #20265353 | 2 |
| #20265350 | 2 |
| #20265294 | 2 |
| #20265292 | 2 |
| #578×C101 | 2 |
| #3290 | 101 |