Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265994 | C2 | semidirect |
| 2. #20265987 | C2 | semidirect |
| 3. #20265978 | C2 | semidirect |
| 4. #20265560 | C2 | semidirect |
| 5. #20265453 | C2 | semidirect |
| 6. #20265439 | C2 | semidirect |
| 7. #20265357 | C2 | semidirect |
| 8. #20265348 | C2 | semidirect |
| 9. #20265293 | C2 | semidirect |
| 10. #20265292 | C2 | semidirect |
| 11. #472×C101 | C2 | semidirect |
| 12. #15692302 | C22 | semidirect |
| 16. #15692288 | C22 | semidirect |
| 27. C2×Dic404 | C22 | semidirect |
| 28. C2×#13108062 | C22 | semidirect |
| 31. #15692263 | C22 | semidirect |
| 33. #15692242 | C22 | semidirect |
| 34. #15692190 | C22 | semidirect |
| 35. #15692182 | C22 | semidirect |
| 37. #15692181 | C22 | semidirect |
| 38. #15692173 | C22 | semidirect |
| 39. C8×Dic101 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C101 | C22 | semidirect |
| 42. #131×C101 | C22 | semidirect |
| 43. #108×C101 | C22 | semidirect |
| 44. #100×C101 | C22 | semidirect |
| 150. C101 | #3290 | semidirect |
| 156. #472 | D101 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D101 | semidirect |
| 185. #131 | C2×D101 | semidirect |
| 188. #108 | C2×D101 | semidirect |
| 193. #100 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265994 | 2 |
| #20265987 | 2 |
| #20265978 | 2 |
| #20265560 | 2 |
| #20265453 | 2 |
| #20265439 | 2 |
| #20265357 | 2 |
| #20265348 | 2 |
| #20265293 | 2 |
| #20265292 | 2 |
| #472×C101 | 2 |
| #3290 | 101 |