Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #20260553 | C2 | direct (N × H) |
| 33. C2×Dic97 | C16 | semidirect |
| 48. Dic97 | C2×C16 | semidirect |
| 49. C2×C97 | C4⋊C16 | semidirect |
| 54. C97 | C2×C4⋊C16 | semidirect |
| 103. C2 | #20260553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095486 | 2 |
| C2×C8×Dic97 | 2 |
| #20260553 | 2 |
| C22×C16×C97 | 2 |
| C2×C4⋊C16 | 97 |