Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 122 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. #20261576 | C2 | semidirect |
| 4. C8×#11715897 | C2 | semidirect |
| 24. #13095495 | C8 | semidirect |
| 31. M16×C97 | C8 | semidirect |
| 46. #11715897 | M16 | direct (N × H) |
| 47. C8×C97 | C2×C8 | semidirect |
| 48. #11715895 | C2×C8 | semidirect |
| 65. C97 | C8×M16 | semidirect |
| 87. M16 | #11715897 | direct (N × H) |
| 113. C8 | C2×#11715897 | 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 |
| #20261576 | 2 |
| C8×#11715897 | 2 |
| M16×Dic97 | 2 |
| C8×M16 | 97 |