Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×#13108064 | C2 | semidirect |
| 3. #20265556 | C2 | semidirect |
| 4. #20265416 | C2 | semidirect |
| 5. #20265387 | C2 | semidirect |
| 6. #20265384 | C2 | semidirect |
| 7. #20265333 | C2 | semidirect |
| 8. #20265332 | C2 | semidirect |
| 9. C4×#13108064 | C2 | semidirect |
| 52. #13108064 | D4 | direct (N × H) |
| 88. D4×C101 | Q16 | semidirect |
| 113. C22×C101 | C2×Q16 | semidirect |
| 120. C4×C101 | C2×Q16 | semidirect |
| 131. C101 | D4×Q16 | semidirect |
| 224. D4 | #13108064 | direct (N × H) |
| 244. C22 | C2×#13108064 | semidirect |
| 254. C4 | C2×#13108064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108064 | 2 |
| D4×Dic202 | 2 |
| #20265556 | 2 |
| #20265416 | 2 |
| #20265387 | 2 |
| #20265384 | 2 |
| #20265333 | 2 |
| #20265332 | 2 |
| C4×#13108064 | 2 |
| D4×#11717579 | 2 |
| D4×Q8×C101 | 2 |
| D4×Q16 | 101 |