Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#15692277 | C2 | semidirect |
| 2. C2×#15692275 | C2 | semidirect |
| 3. #20265723 | C2 | semidirect |
| 4. #20265570 | C2 | semidirect |
| 5. #20265568 | C2 | semidirect |
| 6. #20265565 | C2 | semidirect |
| 7. #20265563 | C2 | semidirect |
| 8. C2×#15692165 | C2 | semidirect |
| 9. C2×#135×C101 | C2 | semidirect |
| 51. C2×#11717579 | D4 | semidirect |
| 68. C2×C8×C101 | D4 | semidirect |
| 117. C101 | #3150 | semidirect |
| 120. C2×#135 | D101 | semidirect |
| 180. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| C2×#15692275 | 2 |
| #20265723 | 2 |
| #20265570 | 2 |
| #20265568 | 2 |
| #20265565 | 2 |
| #20265563 | 2 |
| C2×#15692165 | 2 |
| C2×#135×C101 | 2 |
| #3150 | 101 |