Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20265481 | C2 | semidirect |
| 3. #20265474 | C2 | semidirect |
| 4. #20265469 | C2 | semidirect |
| 5. #20265454 | C2 | semidirect |
| 6. #20265220 | C2 | semidirect |
| 7. C2×#15692188 | C2 | semidirect |
| 8. #20265204 | C2 | semidirect |
| 11. #544×C101 | C2 | semidirect |
| 42. #13108074 | Q8 | semidirect |
| 124. C101 | #3083 | semidirect |
| 125. #544 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265657 | 2 |
| #20265481 | 2 |
| #20265474 | 2 |
| #20265469 | 2 |
| #20265454 | 2 |
| #20265220 | 2 |
| C2×#15692188 | 2 |
| #20265204 | 2 |
| #20265176 | 2 |
| #20265171 | 2 |
| #544×C101 | 2 |
| #3083 | 101 |