Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 146 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. C2×C4×#11715897 | C2 | semidirect |
| 4. #20261601 | C2 | semidirect |
| 7. C22×#11715897 | C4 | semidirect |
| 11. C22⋊#11715897 | C4 | semidirect |
| 33. C22⋊Dic97 | C8 | semidirect |
| 38. C22⋊C4×C97 | C8 | semidirect |
| 47. C2×C4×C97 | C2×C8 | semidirect |
| 55. C2×Dic97 | C2×C8 | semidirect |
| 62. #11715897 | C22⋊C4 | direct (N × H) |
| 67. C22×C97 | C4×C8 | semidirect |
| 86. C97 | C8×C22⋊C4 | semidirect |
| 122. C22⋊C4 | #11715897 | direct (N × H) |
| 145. C2×C4 | C2×#11715897 | semidirect |
| 153. C22 | C4×#11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715897 | 2 |
| C2×C22⋊#11715897 | 2 |
| C2×C4×#11715897 | 2 |
| #20261601 | 2 |
| C22⋊C4×Dic97 | 2 |
| C8×C22⋊C4 | 97 |