Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20265528 | C2 | semidirect |
| 4. #20265514 | C2 | semidirect |
| 5. #20265472 | C2 | semidirect |
| 6. #20265417 | C2 | semidirect |
| 7. #20265387 | C2 | semidirect |
| 8. #20265331 | C2 | semidirect |
| 10. #103×D101 | C2 | semidirect |
| 11. C4×Q16×C101 | C2 | semidirect |
| 91. D404 | Q16 | semidirect |
| 123. C101 | #3299 | semidirect |
| 132. C4×Q16 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265887 | 2 |
| Q8×D404 | 2 |
| #20265528 | 2 |
| #20265514 | 2 |
| #20265472 | 2 |
| #20265417 | 2 |
| #20265387 | 2 |
| #20265331 | 2 |
| C8×D404 | 2 |
| #103×D101 | 2 |
| C4×Q16×C101 | 2 |
| #3299 | 101 |