Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20265654 | C2 | semidirect |
| 3. #20265277 | C2 | semidirect |
| 4. C4×#13108062 | C2 | semidirect |
| 5. #20265213 | C2 | semidirect |
| 6. #20265185 | C2 | semidirect |
| 8. #20265133 | C2 | semidirect |
| 11. C2×#13108062 | C4 | semidirect |
| 16. C4×Dic202 | C22 | semidirect |
| 20. #15692188 | C22 | semidirect |
| 21. #15692186 | C22 | semidirect |
| 22. #15692178 | C22 | semidirect |
| 24. #15692166 | C22 | semidirect |
| 25. C4×#11717579 | C22 | semidirect |
| 34. C2×Dic202 | C2×C4 | semidirect |
| 37. #13108062 | C2×C4 | semidirect |
| 38. #13108062 | C2×C4 | semidirect |
| 40. C2×#11717579 | C2×C4 | semidirect |
| 104. C101 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| #20265654 | 2 |
| #20265277 | 2 |
| C4×#13108062 | 2 |
| #20265213 | 2 |
| #20265185 | 2 |
| #20265182 | 2 |
| #20265133 | 2 |
| #518×C101 | 2 |
| #2949 | 101 |