Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
436 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 154 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. C2×C4×#11715897 | C2 | semidirect |
| 3. #20261601 | C2 | semidirect |
| 6. #15690867 | C4 | direct (N × H) |
| 18. C2×#11715897 | C2×C4 | semidirect |
| 29. C2×C4×D97 | C8 | semidirect |
| 30. C2×C4×D97 | C8 | semidirect |
| 82. C2×D97 | C4×C8 | semidirect |
| 85. C4×C97 | C22⋊C8 | semidirect |
| 87. Dic97 | C22⋊C8 | semidirect |
| 98. C97 | C4×C22⋊C8 | semidirect |
| 186. C4 | #15690867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690867 | 2 |
| C2×C4×#11715897 | 2 |
| #20261601 | 2 |
| C2×C42×D97 | 2 |
| C4×C22⋊C8 | 97 |