Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 90 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. #20261628 | C2 | direct (N × H) |
| 4. #15690884 | C4 | semidirect |
| 6. C2×#13095514 | C4 | semidirect |
| 12. #13095514 | C2×C4 | semidirect |
| 47. C2×C97 | #347 | semidirect |
| 50. C97 | C2×#347 | semidirect |
| 97. C2 | #20261628 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690884 | 2 |
| #20261628 | 2 |
| C2×#15690720 | 2 |
| C2×#347 | 97 |