Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13095501 | C2 | semidirect |
| 3. C2×#15690786 | C2 | semidirect |
| 4. #20260894 | C2 | direct (N × H) |
| 5. C2×#15690735 | C2 | semidirect |
| 6. C2×#15690731 | C2 | semidirect |
| 7. C2×#15690722 | C2 | semidirect |
| 8. C22×SD16×C97 | C2 | semidirect |
| 18. C2×#13095501 | C22 | semidirect |
| 21. #15690786 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690731 | C22 | semidirect |
| 27. #15690722 | C22 | semidirect |
| 31. C2×SD16×C97 | C22 | semidirect |
| 130. C2×C97 | #452 | semidirect |
| 136. C97 | C2×#452 | semidirect |
| 139. C22×SD16 | D97 | semidirect |
| 158. C2×SD16 | C2×D97 | semidirect |
| 267. C2 | #20260894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095510 | 2 |
| C22×#13095501 | 2 |
| C2×#15690786 | 2 |
| #20260894 | 2 |
| C2×#15690735 | 2 |
| C2×#15690731 | 2 |
| C2×#15690722 | 2 |
| C22×SD16×C97 | 2 |
| C2×#452 | 97 |