Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 17. Dic388 | C8 | direct (N × H) |
| 39. C8×C97 | Q16 | semidirect |
| 53. C97 | C8×Q16 | semidirect |
| 93. C8 | Dic388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic194 | 2 |
| C4×Dic388 | 2 |
| #20260488 | 2 |
| #20260467 | 2 |
| C82×C97 | 2 |
| C8×Q16 | 97 |