Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265888 | C2 | semidirect |
| 3. #20265520 | C2 | semidirect |
| 4. #20265492 | C2 | semidirect |
| 5. #20265469 | C2 | semidirect |
| 6. #20265464 | C2 | semidirect |
| 7. #20265424 | C2 | semidirect |
| 8. C4×#13108063 | C2 | semidirect |
| 9. #20265256 | C2 | semidirect |
| 10. #20265218 | C2 | semidirect |
| 11. #500×C101 | C2 | semidirect |
| 122. C101 | #3357 | semidirect |
| 125. #500 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265893 | 2 |
| #20265888 | 2 |
| #20265520 | 2 |
| #20265492 | 2 |
| #20265469 | 2 |
| #20265464 | 2 |
| #20265424 | 2 |
| C4×#13108063 | 2 |
| #20265256 | 2 |
| #20265218 | 2 |
| #500×C101 | 2 |
| #3357 | 101 |