Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. #11762916 | C2 | semidirect |
| 3. Q16×Dic17 | C2 | semidirect |
| 9. C2×Q16×C17 | C4 | semidirect |
| 81. C2×Q16 | Dic17 | semidirect |
| 96. C17 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763287 | 2 |
| #11762916 | 2 |
| Q16×Dic17 | 2 |
| #11762847 | 2 |
| #11762818 | 2 |
| #11762764 | 2 |
| C22×Q16×C17 | 2 |
| #2950 | 17 |