Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#13108074 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. C2×#15692229 | C2 | semidirect |
| 4. #20265324 | C2 | semidirect |
| 5. #20265318 | C2 | semidirect |
| 6. #20265313 | C2 | semidirect |
| 7. #20265179 | C2 | semidirect |
| 8. #407×C101 | C2 | semidirect |
| 13. C2×#13108074 | C22 | semidirect |
| 14. C22×Dic202 | C22 | semidirect |
| 15. C22×D404 | C22 | semidirect |
| 16. C22×D404 | C22 | semidirect |
| 21. C2×#13108063 | C22 | semidirect |
| 22. C2×D808 | C22 | semidirect |
| 26. #15692229 | C22 | semidirect |
| 27. C2×C4⋊Dic101 | C22 | semidirect |
| 29. #15692180 | C22 | semidirect |
| 30. #15692177 | C22 | semidirect |
| 32. C2×M16×C101 | C22 | semidirect |
| 33. C22⋊C8×C101 | C22 | semidirect |
| 34. C22⋊C8×C101 | C22 | semidirect |
| 42. #13108074 | D4 | semidirect |
| 115. D404 | C2×D4 | semidirect |
| 120. Dic202 | C2×D4 | semidirect |
| 131. C22×C101 | AGL(1,ℤ/8) | semidirect |
| 156. C101 | #3006 | semidirect |
| 164. #407 | D101 | semidirect |
| 180. C2×M16 | C2×D101 | semidirect |
| 189. C22⋊C8 | C2×D101 | semidirect |
| 190. C22⋊C8 | C2×D101 | semidirect |
| 295. C22 | #15692283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108074 | 2 |
| C2×#15692283 | 2 |
| C2×#15692229 | 2 |
| #20265324 | 2 |
| #20265318 | 2 |
| #20265313 | 2 |
| #20265179 | 2 |
| #407×C101 | 2 |
| #3006 | 101 |