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×#13095498 | C2 | semidirect |
| 3. C2×#15690786 | C2 | semidirect |
| 4. #20260896 | C2 | direct (N × H) |
| 5. C2×#15690734 | C2 | semidirect |
| 6. C2×#15690732 | C2 | semidirect |
| 7. C2×#15690722 | C2 | semidirect |
| 8. C22×Q16×C97 | C2 | semidirect |
| 18. C2×#13095498 | C22 | semidirect |
| 21. #15690786 | C22 | semidirect |
| 25. #15690734 | C22 | semidirect |
| 26. #15690732 | C22 | semidirect |
| 27. #15690722 | C22 | semidirect |
| 31. C2×Q16×C97 | C22 | semidirect |
| 129. C2×C97 | #452 | semidirect |
| 136. C97 | C2×#452 | semidirect |
| 138. C22×Q16 | D97 | semidirect |
| 156. C2×Q16 | C2×D97 | semidirect |
| 267. C2 | #20260896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095512 | 2 |
| C22×#13095498 | 2 |
| C2×#15690786 | 2 |
| #20260896 | 2 |
| C2×#15690734 | 2 |
| C2×#15690732 | 2 |
| C2×#15690722 | 2 |
| C22×Q16×C97 | 2 |
| C2×#452 | 97 |