Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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. C2×#15692302 | C2 | semidirect |
| 2. #20265975 | C2 | semidirect |
| 3. #20265748 | C2 | semidirect |
| 4. #20265358 | C2 | semidirect |
| 5. #20265348 | C2 | semidirect |
| 6. #20265194 | C2 | semidirect |
| 7. #20265193 | C2 | semidirect |
| 8. C2×#15692173 | C2 | semidirect |
| 9. #575×C101 | C2 | semidirect |
| 21. #15692286 | C22 | semidirect |
| 23. #15692281 | C22 | semidirect |
| 27. #15692253 | C22 | semidirect |
| 28. #15692242 | C22 | semidirect |
| 32. #15692182 | C22 | semidirect |
| 33. #15692181 | C22 | semidirect |
| 34. #15692173 | C22 | semidirect |
| 38. #137×C101 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C101 | C22 | semidirect |
| 186. C101 | #3020 | semidirect |
| 189. #575 | D101 | semidirect |
| 212. #137 | C2×D101 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| #20265975 | 2 |
| #20265748 | 2 |
| #20265358 | 2 |
| #20265348 | 2 |
| #20265194 | 2 |
| #20265193 | 2 |
| C2×#15692173 | 2 |
| #575×C101 | 2 |
| #3020 | 101 |