Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 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. #20265527 | C2 | semidirect |
| 3. #20265510 | C2 | semidirect |
| 4. #20265472 | C2 | semidirect |
| 5. #20265416 | C2 | semidirect |
| 6. #20265384 | C2 | semidirect |
| 7. #20265333 | C2 | semidirect |
| 8. C4×#13108064 | C2 | semidirect |
| 10. C2×#15692179 | C2 | semidirect |
| 82. D4×C101 | Q16 | semidirect |
| 123. C101 | #3299 | semidirect |
| 208. D4 | #13108064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265884 | 2 |
| #20265527 | 2 |
| #20265510 | 2 |
| #20265472 | 2 |
| #20265416 | 2 |
| #20265384 | 2 |
| #20265333 | 2 |
| C4×#13108064 | 2 |
| D4×#11717579 | 2 |
| C2×#15692179 | 2 |
| D4×Q8×C101 | 2 |
| #3299 | 101 |