Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11763537 | C2 | semidirect |
| 3. #11763164 | C2 | semidirect |
| 5. #11763110 | C2 | semidirect |
| 6. #11763095 | C2 | semidirect |
| 7. #11763032 | C2 | semidirect |
| 9. C4×Dic68 | C2 | semidirect |
| 10. C4×#63219 | C2 | semidirect |
| 11. C8×Q8×C17 | C2 | semidirect |
| 122. C8×Q8 | D17 | semidirect |
| 158. C17 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763537 | 2 |
| #11763164 | 2 |
| #11763156 | 2 |
| #11763110 | 2 |
| #11763095 | 2 |
| #11763032 | 2 |
| #11763010 | 2 |
| C4×Dic68 | 2 |
| C4×#63219 | 2 |
| C8×Q8×C17 | 2 |
| #3365 | 17 |