Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692280 | C2 | semidirect |
| 2. C2×#15692280 | C2 | semidirect |
| 3. #20265944 | C2 | semidirect |
| 4. #20265445 | C2 | semidirect |
| 5. #20265442 | C2 | semidirect |
| 6. #20265225 | C2 | semidirect |
| 7. #20265161 | C2 | semidirect |
| 8. C2×#15692171 | C2 | semidirect |
| 9. #575×C101 | C2 | semidirect |
| 16. C2×#13108061 | C22 | semidirect |
| 18. C2×#13108059 | C22 | semidirect |
| 20. #15692262 | C22 | semidirect |
| 25. #15692190 | C22 | semidirect |
| 26. #15692174 | C22 | semidirect |
| 27. #15692172 | C22 | semidirect |
| 28. #15692171 | C22 | semidirect |
| 32. #137×C101 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C101 | C22 | semidirect |
| 148. C101 | #3068 | semidirect |
| 149. #575 | D101 | semidirect |
| 162. #137 | C2×D101 | semidirect |
| 168. 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×#15692280 | 2 |
| #20265944 | 2 |
| #20265445 | 2 |
| #20265442 | 2 |
| #20265225 | 2 |
| #20265161 | 2 |
| C2×#15692171 | 2 |
| #575×C101 | 2 |
| #3068 | 101 |