Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
| 4. #20265416 | C2 | direct (N × H) |
| 5. C2×#15692188 | C2 | semidirect |
| 6. C2×#15692179 | C2 | semidirect |
| 7. C2×#15692178 | C2 | semidirect |
| 11. C2×#13108064 | C22 | semidirect |
| 21. #15692188 | C22 | semidirect |
| 22. #15692179 | C22 | semidirect |
| 23. #15692178 | C22 | semidirect |
| 66. C23×C101 | Q16 | semidirect |
| 99. C22×C101 | C2×Q16 | semidirect |
| 111. C2×C101 | #467 | semidirect |
| 116. C101 | C2×#467 | semidirect |
| 182. C23 | #13108064 | semidirect |
| 215. C22 | C2×#13108064 | semidirect |
| 227. C2 | #20265416 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108064 | 2 |
| C23×#11717579 | 2 |
| C2×#15692234 | 2 |
| #20265416 | 2 |
| C2×#15692188 | 2 |
| C2×#15692179 | 2 |
| C2×#15692178 | 2 |
| C2×C22⋊Q8×C101 | 2 |
| C2×#467 | 101 |