Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13108062 | C2 | semidirect |
| 2. #20265748 | C2 | semidirect |
| 3. #20265652 | C2 | semidirect |
| 4. #20265390 | C2 | semidirect |
| 5. #20265380 | C2 | semidirect |
| 6. #20265205 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 8. #20265173 | C2 | semidirect |
| 14. #15692253 | C22 | semidirect |
| 15. #15692242 | C22 | semidirect |
| 23. #15692184 | C22 | semidirect |
| 24. #15692180 | C22 | semidirect |
| 25. #15692179 | C22 | semidirect |
| 26. #15692176 | C22 | semidirect |
| 117. C101 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| #20265748 | 2 |
| #20265652 | 2 |
| #20265390 | 2 |
| #20265380 | 2 |
| #20265205 | 2 |
| #20265187 | 2 |
| #20265173 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #3042 | 101 |