Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×D68 | C2 | semidirect |
| 3. #11763161 | C2 | semidirect |
| 4. #11763152 | C2 | semidirect |
| 5. #11763056 | C2 | semidirect |
| 6. #11763015 | C2 | semidirect |
| 7. #11762949 | C2 | semidirect |
| 8. C4×#63230 | C2 | semidirect |
| 9. #11762886 | C2 | semidirect |
| 10. #11762816 | C2 | semidirect |
| 11. C17×#477 | C2 | semidirect |
| 126. #477 | D17 | semidirect |
| 167. C17 | #3329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763525 | 2 |
| Q8×D68 | 2 |
| #11763161 | 2 |
| #11763152 | 2 |
| #11763056 | 2 |
| #11763015 | 2 |
| #11762949 | 2 |
| C4×#63230 | 2 |
| #11762886 | 2 |
| #11762816 | 2 |
| C17×#477 | 2 |
| #3329 | 17 |