Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
| 4. #20265274 | C2 | semidirect |
| 5. #20265268 | C2 | semidirect |
| 6. #20265213 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 8. #20265135 | C2 | semidirect |
| 11. C2×#13108062 | C4 | semidirect |
| 16. #15692220 | C22 | semidirect |
| 23. #15692188 | C22 | semidirect |
| 24. #15692186 | C22 | semidirect |
| 25. #15692180 | C22 | semidirect |
| 26. #15692165 | C22 | semidirect |
| 27. C8×Dic101 | C22 | semidirect |
| 34. C2×Dic202 | C2×C4 | semidirect |
| 38. #13108062 | C2×C4 | semidirect |
| 39. #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 |
| #20265652 | 2 |
| #20265274 | 2 |
| #20265268 | 2 |
| #20265213 | 2 |
| #20265187 | 2 |
| #20265135 | 2 |
| #418×C101 | 2 |
| #2949 | 101 |