Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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. C2×#15690889 | C2 | semidirect |
| 2. #20261716 | C2 | direct (N × H) |
| 3. C2×#15690869 | C2 | semidirect |
| 6. #15690889 | C22 | semidirect |
| 10. #15690869 | C22 | semidirect |
| 14. C2×#13095512 | C4 | semidirect |
| 16. C22×D388 | C4 | semidirect |
| 18. C22×C4×D97 | C4 | semidirect |
| 20. C22×Q8×C97 | C4 | semidirect |
| 37. C2×D388 | C2×C4 | semidirect |
| 44. C2×C4×D97 | C2×C4 | semidirect |
| 51. C2×Q8×C97 | C2×C4 | semidirect |
| 107. C2×C97 | #410 | semidirect |
| 113. C97 | C2×#410 | semidirect |
| 123. C22×Q8 | #87604 | semidirect |
| 142. C2×Q8 | C2×#87604 | semidirect |
| 223. C2 | #20261716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690889 | 2 |
| #20261716 | 2 |
| C2×#15690869 | 2 |
| C22×#13095512 | 2 |
| C2×#410 | 97 |