Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 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 |
|---|---|---|
| 2. C2×#15692288 | C2 | semidirect |
| 3. #20265748 | C2 | semidirect |
| 4. #20265362 | C2 | semidirect |
| 5. #20265357 | C2 | semidirect |
| 6. #20265193 | C2 | semidirect |
| 7. #413×C101 | C2 | semidirect |
| 16. C22×Dic202 | C22 | semidirect |
| 18. #15692288 | C22 | semidirect |
| 21. #15692253 | C22 | semidirect |
| 22. #15692242 | C22 | semidirect |
| 25. #15692214 | C22 | semidirect |
| 26. #15692181 | C22 | semidirect |
| 28. C2×M16×C101 | C22 | semidirect |
| 29. #101×C101 | C22 | semidirect |
| 30. #100×C101 | C22 | semidirect |
| 130. C101 | #3022 | semidirect |
| 137. #413 | D101 | semidirect |
| 152. C2×M16 | C2×D101 | semidirect |
| 159. #101 | C2×D101 | semidirect |
| 160. #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 |
| C2×#15692288 | 2 |
| #20265748 | 2 |
| #20265362 | 2 |
| #20265357 | 2 |
| #20265193 | 2 |
| #413×C101 | 2 |
| #3022 | 101 |