Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. #20261751 | C2 | semidirect |
| 2. C2×C4×#11715897 | C2 | semidirect |
| 3. #20261585 | C2 | semidirect |
| 4. #20261583 | C2 | semidirect |
| 27. #13095511 | C8 | semidirect |
| 68. D388 | C2×C8 | semidirect |
| 73. Dic194 | C2×C8 | semidirect |
| 99. C97 | #1476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261751 | 2 |
| C2×C4×#11715897 | 2 |
| #20261585 | 2 |
| #20261583 | 2 |
| #20261203 | 2 |
| #1476 | 97 |