Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. Q32×D17 | C2 | semidirect |
| 3. #11762649 | C2 | semidirect |
| 4. #11762648 | C2 | semidirect |
| 5. #11762646 | C2 | semidirect |
| 6. #11762642 | C2 | semidirect |
| 7. C17×Q64 | C2 | semidirect |
| 52. Q64 | D17 | semidirect |
| 70. C17 | #2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763242 | 2 |
| Q32×D17 | 2 |
| #11762649 | 2 |
| #11762648 | 2 |
| #11762646 | 2 |
| #11762642 | 2 |
| C17×Q64 | 2 |
| #2264 | 17 |