Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 32. Q16×C17 | Q8 | semidirect |
| 60. Dic34 | Q16 | direct (N × H) |
| 105. C17 | Q8×Q16 | semidirect |
| 110. Q16 | Dic34 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic34 | 2 |
| #11763214 | 2 |
| #11763213 | 2 |
| #11763104 | 2 |
| #11763102 | 2 |
| C8×Dic34 | 2 |
| Q16×Dic17 | 2 |
| C4×Q16×C17 | 2 |
| Q8×Q16 | 17 |