Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 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. C2×#15692238 | C2 | semidirect |
| 3. #20265092 | C2 | semidirect |
| 4. #20265056 | C2 | semidirect |
| 5. #20265049 | C2 | semidirect |
| 6. #20265033 | C2 | semidirect |
| 7. #20265032 | C2 | semidirect |
| 8. C22×C22⋊C4×C101 | C2 | semidirect |
| 16. C2×#13108053 | C22 | semidirect |
| 18. C2×C22⋊Dic101 | C22 | semidirect |
| 19. C2×C22⋊Dic101 | C22 | semidirect |
| 20. C2×#13108051 | C22 | semidirect |
| 21. C2×#13108051 | C22 | semidirect |
| 22. #15692162 | C22 | semidirect |
| 24. C23×C4×C101 | C22 | semidirect |
| 25. C23×C4×C101 | C22 | semidirect |
| 28. C2×C22⋊C4×C101 | C22 | semidirect |
| 119. C22×C101 | #123 | semidirect |
| 143. C101 | #2405 | semidirect |
| 146. C22×C22⋊C4 | D101 | semidirect |
| 159. C23×C4 | C2×D101 | semidirect |
| 160. C23×C4 | C2×D101 | semidirect |
| 170. C2×C22⋊C4 | C2×D101 | semidirect |
| 268. C22 | #15692238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D101 | 2 |
| C2×#15692238 | 2 |
| #20265092 | 2 |
| #20265056 | 2 |
| #20265049 | 2 |
| #20265033 | 2 |
| #20265032 | 2 |
| C22×C22⋊C4×C101 | 2 |
| #2405 | 101 |