Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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. #20265529 | C2 | semidirect |
| 4. #20265481 | C2 | semidirect |
| 7. #20265387 | C2 | semidirect |
| 8. Q8×#11717579 | C2 | semidirect |
| 9. C4×#13108064 | C2 | semidirect |
| 11. #557×C101 | C2 | semidirect |
| 116. C101 | #3364 | semidirect |
| 117. #557 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265900 | 2 |
| #20265534 | 2 |
| #20265529 | 2 |
| #20265481 | 2 |
| #20265454 | 2 |
| #20265399 | 2 |
| #20265387 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108064 | 2 |
| C4×#13108061 | 2 |
| #557×C101 | 2 |
| #3364 | 101 |