Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20266013 | C2 | semidirect |
| 2. #20265977 | C2 | semidirect |
| 3. #20265723 | C2 | semidirect |
| 4. #20265362 | C2 | semidirect |
| 5. #20265357 | C2 | semidirect |
| 6. #20265352 | C2 | semidirect |
| 7. #20265347 | C2 | semidirect |
| 8. C2×#15692181 | C2 | semidirect |
| 9. #413×C101 | C2 | semidirect |
| 17. C2×#13108074 | C22 | semidirect |
| 20. #15692288 | C22 | semidirect |
| 22. #15692283 | C22 | semidirect |
| 24. #15692253 | C22 | semidirect |
| 25. #15692251 | C22 | semidirect |
| 26. #15692244 | C22 | semidirect |
| 27. #15692242 | C22 | semidirect |
| 30. C2×C4×Dic101 | C22 | semidirect |
| 31. #15692181 | C22 | semidirect |
| 32. #15692181 | C22 | semidirect |
| 34. C2×M16×C101 | C22 | semidirect |
| 35. #101×C101 | C22 | semidirect |
| 36. #100×C101 | C22 | semidirect |
| 45. #13108074 | D4 | semidirect |
| 50. C2×Dic202 | D4 | semidirect |
| 54. C2×D404 | D4 | semidirect |
| 151. C101 | #3018 | semidirect |
| 160. #413 | D101 | semidirect |
| 176. C2×M16 | C2×D101 | semidirect |
| 186. #101 | C2×D101 | semidirect |
| 187. #100 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| #20265977 | 2 |
| #20265723 | 2 |
| #20265362 | 2 |
| #20265357 | 2 |
| #20265352 | 2 |
| #20265347 | 2 |
| C2×#15692181 | 2 |
| #413×C101 | 2 |
| #3018 | 101 |