Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#15692286 | C2 | semidirect |
| 3. C2×#15692286 | C2 | semidirect |
| 4. #20265943 | C2 | semidirect |
| 5. #20265451 | C2 | semidirect |
| 6. #20265443 | C2 | semidirect |
| 7. #20265225 | C2 | semidirect |
| 8. #20265159 | C2 | semidirect |
| 9. C2×#101×C101 | C2 | semidirect |
| 22. C2×#13108064 | C22 | semidirect |
| 24. C2×#13108061 | C22 | semidirect |
| 30. #15692190 | C22 | semidirect |
| 31. #15692173 | C22 | semidirect |
| 32. #15692171 | C22 | semidirect |
| 36. #101×C101 | C22 | semidirect |
| 143. C101 | #3069 | semidirect |
| 152. C2×#101 | D101 | semidirect |
| 178. #101 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265977 | 2 |
| C2×#15692286 | 2 |
| #20265943 | 2 |
| #20265451 | 2 |
| #20265443 | 2 |
| #20265225 | 2 |
| #20265159 | 2 |
| C2×#101×C101 | 2 |
| #3069 | 101 |