Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×#13095519 | C4 | semidirect |
| 11. #15690867 | C4 | semidirect |
| 33. #13095488 | C8 | semidirect |
| 48. C2×C4×C97 | C2×C8 | semidirect |
| 51. C2×Dic97 | C2×C8 | semidirect |
| 61. #11715897 | C22⋊C4 | semidirect |
| 71. C2×D97 | C4×C8 | semidirect |
| 85. C97 | C8×C22⋊C4 | semidirect |
| 143. C2×C4 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| C2×#15690867 | 2 |
| C2×C4×#11715897 | 2 |
| #20261601 | 2 |
| #20260582 | 2 |
| C8×C22⋊C4 | 97 |