Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692285 | C2 | semidirect |
| 3. C22×#13108063 | C2 | semidirect |
| 4. #20265753 | C2 | semidirect |
| 5. #20265342 | C2 | semidirect |
| 6. #20265329 | C2 | semidirect |
| 7. #20265181 | C2 | semidirect |
| 8. #20265143 | C2 | semidirect |
| 9. #416×C101 | C2 | semidirect |
| 15. C22×Dic202 | C22 | semidirect |
| 21. C2×#13108064 | C22 | semidirect |
| 23. C2×#13108063 | C22 | semidirect |
| 24. C2×#13108062 | C22 | semidirect |
| 25. C2×#13108058 | C22 | semidirect |
| 29. #15692235 | C22 | semidirect |
| 30. #15692175 | C22 | semidirect |
| 31. #15692167 | C22 | semidirect |
| 33. C22×C8×C101 | C22 | semidirect |
| 34. #117×C101 | C22 | semidirect |
| 35. #103×C101 | C22 | semidirect |
| 36. #102×C101 | C22 | semidirect |
| 147. C101 | #3009 | semidirect |
| 155. #416 | D101 | semidirect |
| 174. C22×C8 | C2×D101 | semidirect |
| 179. #117 | C2×D101 | semidirect |
| 180. #103 | C2×D101 | semidirect |
| 182. #102 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692301 | 2 |
| C2×#15692285 | 2 |
| C22×#13108063 | 2 |
| #20265753 | 2 |
| #20265342 | 2 |
| #20265329 | 2 |
| #20265181 | 2 |
| #20265143 | 2 |
| #416×C101 | 2 |
| #3009 | 101 |