Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #11762869 | C2 | semidirect |
| 3. #11762865 | C2 | semidirect |
| 4. #11762836 | C2 | semidirect |
| 7. M16×Dic17 | C2 | semidirect |
| 8. C2×#10587486 | C2 | semidirect |
| 9. C17×#424 | C2 | semidirect |
| 94. #424 | D17 | semidirect |
| 123. C17 | #2923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763277 | 2 |
| #11762869 | 2 |
| #11762865 | 2 |
| #11762836 | 2 |
| #11762777 | 2 |
| #11762775 | 2 |
| M16×Dic17 | 2 |
| C2×#10587486 | 2 |
| C17×#424 | 2 |
| #2923 | 17 |