Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
164 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 26. Dic388 | C8 | semidirect |
| 27. #13095501 | C8 | semidirect |
| 29. Q16×C97 | C8 | semidirect |
| 36. #11715906 | Q16 | direct (N × H) |
| 58. C97 | C8×Q16 | semidirect |
| 77. Q16 | #11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715906 | 2 |
| #20261825 | 2 |
| Q8⋊#11715906 | 2 |
| C8×#11715906 | 2 |
| Q16×#87604 | 2 |
| C8×Q16 | 97 |