Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #11762578 | C2 | semidirect |
| 4. #11762577 | C2 | semidirect |
| 5. C17×#343 | C2 | semidirect |
| 14. M16×D17 | C4 | semidirect |
| 87. #343 | D17 | semidirect |
| 107. C17 | #1742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D17 | 2 |
| C2×#10587578 | 2 |
| #11762578 | 2 |
| #11762577 | 2 |
| C17×#343 | 2 |
| #1742 | 17 |