Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265573 | C2 | semidirect |
| 3. #20265518 | C2 | semidirect |
| 4. #20265505 | C2 | semidirect |
| 5. #20265472 | C2 | semidirect |
| 6. #20265459 | C2 | semidirect |
| 7. #20265433 | C2 | semidirect |
| 8. C4×#13108064 | C2 | semidirect |
| 10. #20265220 | C2 | semidirect |
| 117. C101 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265884 | 2 |
| #20265573 | 2 |
| #20265518 | 2 |
| #20265505 | 2 |
| #20265472 | 2 |
| #20265459 | 2 |
| #20265433 | 2 |
| C4×#13108064 | 2 |
| #20265255 | 2 |
| #20265220 | 2 |
| #556×C101 | 2 |
| #3356 | 101 |